276 results on '"Yasuhiro Hatsugai"'
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2. Non-Hermitian topology in rock–paper–scissors games
- Author
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Tsuneya Yoshida, Tomonari Mizoguchi, and Yasuhiro Hatsugai
- Subjects
Medicine ,Science - Abstract
Abstract Non-Hermitian topology is a recent hot topic in condensed matters. In this paper, we propose a novel platform drawing interdisciplinary attention: rock–paper–scissors (RPS) cycles described by the evolutionary game theory. Specifically, we demonstrate the emergence of an exceptional point and a skin effect by analyzing topological properties of their payoff matrix. Furthermore, we discover striking dynamical properties in an RPS chain: the directive propagation of the population density in the bulk and the enhancement of the population density only around the right edge. Our results open new avenues of the non-Hermitian topology and the evolutionary game theory.
- Published
- 2022
- Full Text
- View/download PDF
3. Higher-order topological Mott insulator on the pyrochlore lattice
- Author
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Yuichi Otsuka, Tsuneya Yoshida, Koji Kudo, Seiji Yunoki, and Yasuhiro Hatsugai
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Medicine ,Science - Abstract
Abstract We provide the first unbiased evidence for a higher-order topological Mott insulator in three dimensions by numerically exact quantum Monte Carlo simulations. This insulating phase is adiabatically connected to a third-order topological insulator in the noninteracting limit, which features gapless modes around the corners of the pyrochlore lattice and is characterized by a $${\mathbb {Z}}_{4}$$ Z 4 spin-Berry phase. The difference between the correlated and non-correlated topological phases is that in the former phase the gapless corner modes emerge only in spin excitations being Mott-like. We also show that the topological phase transition from the third-order topological Mott insulator to the usual Mott insulator occurs when the bulk spin gap solely closes.
- Published
- 2021
- Full Text
- View/download PDF
4. Bulk-edge correspondence of classical diffusion phenomena
- Author
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Tsuneya Yoshida and Yasuhiro Hatsugai
- Subjects
Medicine ,Science - Abstract
Abstract We elucidate that diffusive systems, which are widely found in nature, can be a new platform of the bulk-edge correspondence, a representative topological phenomenon. Using a discretized diffusion equation, we demonstrate the emergence of robust edge states protected by the winding number for one- and two-dimensional systems. These topological edge states can be experimentally accessible by measuring diffusive dynamics at edges. Furthermore, we discover a novel diffusion phenomenon by numerically simulating the distribution of temperatures for a honeycomb lattice system; the temperature field with wavenumber $$\pi $$ π cannot diffuse to the bulk, which is attributed to the complete localization of the edge state.
- Published
- 2021
- Full Text
- View/download PDF
5. Interaction-induced topological charge pump
- Author
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Yoshihito Kuno and Yasuhiro Hatsugai
- Subjects
Physics ,QC1-999 - Abstract
Based on a topological transition of the symmetry-protected topological phase (SPT), an interaction-induced topological charge pump (iTCP) is proposed with the symmetry-breaking parameter as a synthetic dimension. It implies that the phase boundary of the SPT is a topological obstruction, although iTCP and the gap closing singularity are stable for symmetry-breaking perturbations. As for the iTCP, an interaction is essential since the pumped charge is trivial for a noninteracting system. We have confirmed the bulk-edge correspondence for this iTCP using density matrix renormalization group for the Rice-Mele model with nearest-neighbor interactions. As for a realization in optical lattices, an interaction sweeping pump protocol is proposed as well.
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- 2020
- Full Text
- View/download PDF
6. Fate of fractional quantum Hall states in open quantum systems: Characterization of correlated topological states for the full Liouvillian
- Author
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Tsuneya Yoshida, Koji Kudo, Hosho Katsura, and Yasuhiro Hatsugai
- Subjects
Physics ,QC1-999 - Abstract
Despite previous extensive analysis of open quantum systems described by the Lindblad equation, it is unclear whether correlated topological states, such as fractional quantum Hall states, are maintained even in the presence of the jump term. In this paper, we introduce the pseudospin Chern number of the Liouvillian which is computed by twisting the boundary conditions only for one of the subspaces of the doubled Hilbert space. The existence of such a topological invariant elucidates that the topological properties remain unchanged even in the presence of the jump term, which does not close the gap of the effective non-Hermitian Hamiltonian (obtained by neglecting the jump term). In other words, the topological properties are encoded into an effective non-Hermitian Hamiltonian rather than the full Liouvillian. This is particularly useful when the jump term can be written as a strictly block-upper (-lower) triangular matrix in the doubled Hilbert space, in which case the presence or absence of the jump term does not affect the spectrum of the Liouvillian. With the pseudospin Chern number, we address the characterization of fractional quantum Hall states with two-body loss but without gain, elucidating that the topology of the non-Hermitian fractional quantum Hall states is preserved even in the presence of the jump term. This numerical result also supports the use of the non-Hermitian Hamiltonian which significantly reduces the numerical cost. Similar topological invariants can be extended to treat correlated topological states for other spatial dimensions and symmetry (e.g., one-dimensional open quantum systems with inversion symmetry), indicating the high versatility of our approach.
- Published
- 2020
- Full Text
- View/download PDF
7. Mirror skin effect and its electric circuit simulation
- Author
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Tsuneya Yoshida, Tomonari Mizoguchi, and Yasuhiro Hatsugai
- Subjects
Physics ,QC1-999 - Abstract
We analyze the impacts of crystalline symmetry on non-Hermitian skin effects. Focusing on mirror symmetry, we propose another type of skin effect, a mirror skin effect, which results in a significant dependence of the energy spectrum on the boundary condition only for the mirror invariant line in the two-dimensional Brillouin zone. This effect arises from the topological properties characterized by a mirror winding number. We further reveal that the mirror skin effect can be observed for an electric circuit composed of negative impedance converters with a current inversion where switching the boundary condition significantly changes the admittance eigenvalues only along the mirror invariant lines. Furthermore, we demonstrate that extensive localization of the eigenstates for each mirror sector results in an anomalous voltage response.
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- 2020
- Full Text
- View/download PDF
8. Z_{Q} Berry phase for higher-order symmetry-protected topological phases
- Author
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Hiromu Araki, Tomonari Mizoguchi, and Yasuhiro Hatsugai
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Physics ,QC1-999 - Abstract
We propose the Z_{Q} Berry phase as a topological invariant for higher-order symmetry-protected topological (HOSPT) phases for two- and three-dimensional systems. It is topologically stable for electron-electron interactions assuming the gap remains open. As a concrete example, we show that the Berry phase is quantized in Z_{4} and characterizes the HOSPT phase of the extended Benalcazar-Bernevig-Hughes (BBH) model, which contains the next-nearest-neighbor hopping and the intersite Coulomb interactions. In addition, we introduce the Z_{4} Berry phase for the spin-model analog of the BBH model. Furthermore, we demonstrate the Berry phase is quantized in Z_{4} for the three-dimensional version of the BBH model. We also confirm the bulk-corner correspondence between the Z_{4} Berry phase and the corner states in the HOSPT phases.
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- 2020
- Full Text
- View/download PDF
9. Edge states of mechanical diamond and its topological origin
- Author
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Yuta Takahashi, Toshikaze Kariyado, and Yasuhiro Hatsugai
- Subjects
winding number ,edge states ,bulk-edge correspondence ,Berry phase ,Science ,Physics ,QC1-999 - Abstract
A mechanical diamond, with the classical mechanics of a spring-mass model arrayed on a diamond lattice, is discussed topologically. Its frequency dispersion possesses an intrinsic nodal structure in the three-dimensional Brillouin zone (BZ) protected by the chiral symmetry. Topological changes of the line nodes are demonstrated, associated with the modification of the tension. The line nodes projected into two-dimensional BZ, form loops, which are characterized by the quantized Berry phases with 0 or π . With boundaries, the edge states are discussed in relation to the Berry phases and winding numbers, and the bulk-edge correspondence of the mechanical diamond is established.
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- 2017
- Full Text
- View/download PDF
10. Mass-controlled Topological Edge States in Two Dimensions
- Author
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Tohru Kawarabayashi and Yasuhiro Hatsugai
- Published
- 2023
11. Higher-Order Topological Insulator on a Martini Lattice and Its Square Root Descendant
- Author
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Daiki Matsumoto, Tomonari Mizoguchi, and Yasuhiro Hatsugai
- Subjects
Condensed Matter - Mesoscale and Nanoscale Physics ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,FOS: Physical sciences ,General Physics and Astronomy - Abstract
Notion of square-root topological insulators have been recently generalized to higher-order topological insulators. In two-dimensional square-root higher-order topological insulators, emergence of in-gap corner states are inherited from the squared Hamiltonian which hosts higher-order topology. In this paper, we propose that the martini lattice model serves as a concrete example of higher-order topological insulators. Furthermore, we also propose a suquare-root higher-order topological insulator based on the martini model. Specifically, we propose that the honeycomb lattice model with two-site decoration, whose squared Hamiltonian consists of two martini lattice models, realizes square-root higher-order topological insulators. We show, for both of these two models, that in-gap corner states appear at finite energies and that they are portected by non-trivial bulk $\mathbb{Z}_3$ topological invariant., Comment: 10 pages, 10 figures
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- 2023
12. Unconventional gapless semiconductor in an extended martini lattice in covalent honeycomb materials
- Author
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Tomonari Mizoguchi, Yanlin Gao, Mina Maruyama, Yasuhiro Hatsugai, and Susumu Okada
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Condensed Matter - Materials Science ,Condensed Matter - Strongly Correlated Electrons ,Condensed Matter - Mesoscale and Nanoscale Physics ,Strongly Correlated Electrons (cond-mat.str-el) ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Materials Science (cond-mat.mtrl-sci) ,FOS: Physical sciences - Abstract
We study characteristic electronic structures in an extended martini lattice model and propose its materialization in $\pi$-electron networks constructed by designated chemisorption on graphene and silicene. By investigating the minimal tight-binding model, we reveal rich electronic structures tuned by the ratio of hopping parameters, ranging from the band insulator to the unconventional gapless semiconductor. Remarkably, the unconventional gapless semiconductor is characterized by a flat band at the Fermi level. Further, the density functional theory calculations for candidate materials reveal that the characteristic electronic structures can be realized by designated chemisorption or chemical substitution on graphene and silicene, and that the electronic structure near the Fermi level is tunable by the choice of the atomic species of adsorbed atoms. Our results open the way to search exotic electronic structures and their functionalities induced by an extended martini lattice., Comment: 6 pages, 4 figures for the main text, 5 pages, 5 figures for Supplemental Material
- Published
- 2023
13. Molecular-orbital representation with random U(1) variables
- Author
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Yasuhiro Hatsugai and Tomonari Mizoguchi
- Subjects
Condensed Matter - Mesoscale and Nanoscale Physics ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,FOS: Physical sciences ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Condensed Matter - Disordered Systems and Neural Networks - Abstract
We propose random tight-binding models that host macroscopically degenerate zero energy modes and belong to the unitary class. Specifically, we employ the molecular-orbital representation, where a Hamiltonian is constructed by a set of non-orthogonal orbitals composed of linear combinations of atomic orbitals. By setting the coefficients appearing in molecular orbitals to be random U(1) variables, we can make the models belong to the unitary class. We find two characteristic behaviors that are distinct from the random-real-valued molecular-orbital model. Firstly, a finite energy gap opens on top of the degenerate zero energy modes. Secondly, besides the zero energy modes, we also argue that the band center of the finite energy modes is critical, which is inherited from the dual counterpart, namely, the random-phase model on a bipartite lattice. Furthermore, as a by-product of this model-construction scheme, we also construct the random tight-binding model on a composite lattice, where we also find a realization of critical states., 11 pages, 13 figures
- Published
- 2023
14. Fate of exceptional points under interactions: Reduction of topological classifications
- Author
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Tsuneya Yoshida and Yasuhiro Hatsugai
- Subjects
Condensed Matter - Other Condensed Matter ,Condensed Matter - Strongly Correlated Electrons ,Quantum Physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Strongly Correlated Electrons (cond-mat.str-el) ,Quantum Gases (cond-mat.quant-gas) ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,FOS: Physical sciences ,Condensed Matter - Quantum Gases ,Quantum Physics (quant-ph) ,Other Condensed Matter (cond-mat.other) - Abstract
Despite recent extensive studies of the non-Hermitian topology, understanding interaction effects is left as a crucial question. In this paper, we address interaction effects on exceptional points which are protected by the non-trivial point-gap topology unique to non-Hermitian systems. Our analysis in a two-dimensional parameter space elucidates the existence of exceptional points and symmetry-protected exceptional rings fragile against interactions; they are topologically protected only in non-interacting cases. This fragility of exceptional points and symmetry-protected exceptional rings arises from the reduction of non-Hermitian topological classifications, which is elucidated by introducing topological invariants of the second-quantized Hamiltonian for both non-interacting and interacting cases. These topological invariants are also available to analyze the reduction phenomena of gapped systems. The above results strongly suggest similar reduction phenomena of exceptional points in generic cases and open up a new direction of research in the non-Hermitian topology., Comment: 14 pages, 12 figures, published in PRB
- Published
- 2023
15. Reduction of one-dimensional non-Hermitian point-gap topology by interactions
- Author
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Tsuneya Yoshida and Yasuhiro Hatsugai
- Subjects
Quantum Physics ,Condensed Matter - Strongly Correlated Electrons ,Condensed Matter - Mesoscale and Nanoscale Physics ,Statistical Mechanics (cond-mat.stat-mech) ,Strongly Correlated Electrons (cond-mat.str-el) ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,FOS: Physical sciences ,Quantum Physics (quant-ph) ,Condensed Matter - Statistical Mechanics - Abstract
In spite of extensive works on the non-Hermitian topology, correlations effects remain crucial questions. We hereby analyze correlated non-Hermitian systems with special emphasis on the one-dimensional point-gap topology. Specifically, our analysis elucidates that correlations result in reduction of the topological classification $\mathbb{Z}\times \mathbb{Z} \to \mathbb{Z}$ for systems of one synthetic dimension with charge $\mathrm{U(1)}$ symmetry and spin-parity symmetry. Furthermore, we analyze an extended Hatano-Nelson chain which exhibits striking correlation effects; correlations destroy the skin effect at the non-interacting level. This fragility of the skin effect against interactions is consistent with the reduction of the point-gap topology in the one spatial dimension. The above discoveries shed new light on the topology of correlated systems and open up new directions of researches on non-Hermitian topological physics., Comment: 14 pages and 10 figures
- Published
- 2022
16. Adiabatic continuity of the spinful quantum Hall states
- Author
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Koji Kudo and Yasuhiro Hatsugai
- Subjects
Condensed Matter - Strongly Correlated Electrons ,Strongly Correlated Electrons (cond-mat.str-el) ,FOS: Physical sciences ,Condensed Matter::Strongly Correlated Electrons - Abstract
By using the extended Hubbard model of anyons, we numerically demonstrate the adiabatic deformation of the spinful quantum Hall (QH) states by transmutation of statistical fluxes. While the ground state is always spin-polarized in a series of $\nu=1$ integer QH system, the adiabatic continuity between the singlet QH states at $\nu=2$ and $\nu=2/5$ is confirmed. These results are consistent with the composite fermion theory with spin. The many-body Chern number of the ground state multiplet works as an adiabatic invariant and also explains the wild change of the topological degeneracy during the evolution. The generalized Streda formula of spinful systems is justified., Comment: 8 pages, 5 figures
- Published
- 2022
17. Discriminant indicator with generalized rotational symmetry
- Author
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Hiromasa Wakao, Tsuneya Yoshida, and Yasuhiro Hatsugai
- Subjects
Condensed Matter - Mesoscale and Nanoscale Physics ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,FOS: Physical sciences - Abstract
Discriminant indicators with generalized inversion symmetry are computed only from data at the high-symmetry points. They allow a systematic search for exceptional points. In this paper, we propose discriminant indicators for two- and three-dimensional systems with generalized $n$-fold rotational symmetry ($n=4$, $6$). As is the case for generalized inversion symmetry, the indicator taking a nontrivial value predicts the emergence of exceptional points and loops without ambiguity of the reference energy. A distinct difference from the case of generalized inversion symmetry is that the indicator with generalized $n$-fold rotational symmetry ($n=4$, $6$) can be computed only from data at two of four high-symmetry points in the two-dimensional Brillouin zone. Such a difference is also observed in three-dimensional systems. Furthermore, we also propose how to fabricate a two-dimensional system with generalized four-fold rotational symmetry for an electrical circuit., 11 pages, 10 figures, references updated
- Published
- 2022
18. Construction of interacting flat-band models by molecular-orbital representation: Correlation functions, energy gap, and entanglement
- Author
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Tomonari Mizoguchi, Yoshihito Kuno, and Yasuhiro Hatsugai
- Subjects
Condensed Matter - Strongly Correlated Electrons ,Strongly Correlated Electrons (cond-mat.str-el) ,Statistical Mechanics (cond-mat.stat-mech) ,Quantum Gases (cond-mat.quant-gas) ,FOS: Physical sciences ,General Physics and Astronomy ,Condensed Matter - Quantum Gases ,Condensed Matter - Statistical Mechanics - Abstract
We calculate correlation functions of exactly-solvable one-dimensional flat-band models by utilizing the "molecular-orbital" representation. The models considered in this paper have a gapped ground state with flat-band being fully occupied, even in the presence of the interaction. In this class of models, the space spanned by the "molecular-orbitals" is the co-space of that spanned by the flat bands. Thanks to this property, the correlation functions are calculated by using the information of the molecular-orbitals rather than the explicit forms of the flat-band wave functions, which simplifies the calculations. As a demonstration, several one-dimensional models and their correlation functions are presented. We also calculate the entanglement entropy by using the correlation function., 17 pages, 6 figures
- Published
- 2022
19. Bulk-edge correspondence in the adiabatic heuristic principle
- Author
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Koji Kudo, Yoshihito Kuno, and Yasuhiro Hatsugai
- Subjects
Condensed Matter - Strongly Correlated Electrons ,Strongly Correlated Electrons (cond-mat.str-el) ,Condensed Matter - Mesoscale and Nanoscale Physics ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,FOS: Physical sciences ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect - Abstract
Using the Laughlin's argument on a torus with two pin-holes, we numerically demonstrate that the discontinuities of the center-of-mass work well as an invariant of the pumping phenomena during the process of the flux-attachment, trading the magnetic flux for the statistical one. This is consistent with the bulk-edge correspondence of the fractional quantum Hall effect of anyons. We also confirm that the general feature of the edge states remains unchanged during the process while the topological degeneracy is discretely changed. This supports the stability of the quantum Hall edge states in the adiabatic heuristic principle., 7 pages, 5 figures
- Published
- 2021
20. Competition of First-Order and Second-Order Topology on the Honeycomb Lattice
- Author
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Stephan Rachel, Yasuhiro Hatsugai, Matthew Bunney, and Tomonari Mizoguchi
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Condensed Matter - Mesoscale and Nanoscale Physics ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,FOS: Physical sciences ,Condensed Matter::Strongly Correlated Electrons - Abstract
We investigate both first-order topology, as realized through Haldane's model, and second-order topology, implemented through an additional Kekul\'e-distortion, on the honeycomb lattice. The interplay and competition of both terms result in a phase diagram at half-filling which contains twelve distinct phases. All phases can be characterized by the first Chern number or by a quantized $\mathbb{Z}_Q$ Berry phase. Highlights include phases with high Chern numbers, a novel $\mathbb{Z}_6$ topological phase, but also coupled kagome-lattice Chern insulators. Furthermore, we explore the insulating phases at lower fillings, and find again first-order and second-order topological phases. Finally, we identify real-space structures which feature corner states not only at half but also at third and sixth fillings, in agreement with the quantized $\mathbb{Z}_Q$ Berry phases., Comment: 19 pages, 14 figures
- Published
- 2021
21. Symmetry-Protected Multifold Exceptional Points and Their Topological Characterization
- Author
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Pierre Delplace, Yasuhiro Hatsugai, Tsuneya Yoshida, Laboratoire de Physique de l'ENS Lyon (Phys-ENS), École normale supérieure de Lyon (ENS de Lyon)-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Université de Tsukuba = University of Tsukuba, ANR-16-IDEX-0005,IDEXLYON,IDEXLYON(2016), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), and Université de Lyon-Université de Lyon
- Subjects
Physics ,Quantum Physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Homotopy ,Fluid Dynamics (physics.flu-dyn) ,FOS: Physical sciences ,General Physics and Astronomy ,Antiunitary operator ,Parity (physics) ,Physics - Fluid Dynamics ,Parameter space ,Characterization (mathematics) ,Topology ,01 natural sciences ,Stability (probability) ,010305 fluids & plasmas ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,0103 physical sciences ,Homogeneous space ,Symmetry (geometry) ,Quantum Physics (quant-ph) ,010306 general physics ,[PHYS.COND.CM-MSQHE]Physics [physics]/Condensed Matter [cond-mat]/Mesoscopic Systems and Quantum Hall Effect [cond-mat.mes-hall] - Abstract
We investigate the existence of higher order exceptional points (EPs) in non-Hermitian systems, and show that $\mu$-fold EPs are stable in $\mu-1$ dimensions in the presence of anti-unitary symmetries that are local in parameter space, such as e.g. PT or CP symmetries. This implies in particular that 3-fold and 4-fold symmetry-protected EPs are stable respectively in 2 and 3 dimensions. The stability of such exceptional points is expressed in terms of the homotopy properties of a "resultant vector" that we introduce. Our framework also allows us to rephrase the previously proposed $\mathbb{Z}_2$ index of PT and CP symmetric gapped phases beyond the realm of two-band models. We apply this general formalism to a frictional shallow water model that is found to exhibit 3-fold exceptional points associated with topological numbers $\pm1$. For this model, we also show different non-Hermitian topological transitions associated with these exceptional points, such as their merging and a transition to a regime where propagation becomes forbidden., Comment: accepted version to Phys. Rev. Lett
- Published
- 2021
22. Non-Hermitian topology in rock-paper-scissors games
- Author
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Tsuneya Yoshida, Yasuhiro Hatsugai, and Tomonari Mizoguchi
- Subjects
Physics - Physics and Society ,Multidisciplinary ,Statistical Mechanics (cond-mat.stat-mech) ,Condensed Matter - Mesoscale and Nanoscale Physics ,Evolution ,Science ,FOS: Physical sciences ,Physics and Society (physics.soc-ph) ,Condensed Matter - Soft Condensed Matter ,Article ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Medicine ,Soft Condensed Matter (cond-mat.soft) ,Quantitative Biology::Populations and Evolution ,Topological insulators ,Biological physics ,Condensed Matter - Statistical Mechanics - Abstract
Non-Hermitian topology is a recent hot topic in condensed matters. In this paper, we propose a novel platform drawing interdisciplinary attention: rock-paper-scissors (RPS) cycles described by the evolutionary game theory. Specifically, we demonstrate the emergence of an exceptional point and a skin effect by analyzing topological properties of their payoff matrix. Furthermore, we discover striking dynamical properties in an RPS chain: the directive propagation of the population density in the bulk and the enhancement of the population density only around the right edge. Our results open new avenues of the non-Hermitian topology and the evolutionary game theory., 6+6 pages, 4+5 figures
- Published
- 2021
23. Flat band, spin-1 Dirac cone, and Hofstadter diagram in the fermionic square kagome model
- Author
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Yasuhiro Hatsugai, Tomonari Mizoguchi, and Yoshihito Kuno
- Subjects
Physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,High Energy Physics::Lattice ,Dirac (software) ,Diagram ,FOS: Physical sciences ,Fermion ,Square (algebra) ,symbols.namesake ,Quantum mechanics ,Lattice (order) ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,symbols ,Hamiltonian (quantum mechanics) ,Eigenvalues and eigenvectors ,Spin-½ - Abstract
We study characteristic band structures of the fermions on a square kagome lattice, one of the two-dimensional lattices hosting a corner-sharing network of triangles. We show that the band structures of the nearest-neighbor tight-binding model exhibit many characteristic features, including a flat band which is ubiquitous among frustrated lattices. On the flat band, we elucidate its origin by using the molecular-orbital representation and also find localized exact eigenstates called compact localized states. In addition to the flat band, we also find two spin-1 Dirac cones with different energies. These spin-1 Dirac cones are not described by the simplest effective Dirac Hamiltonian because the middle band is bended and the energy spectrum is particle-hole asymmetric. We also investigated the Hofstadter problem on a square kagome lattice in the presence of an external field and find that the profile of the Chern numbers around the modified spin-1 Dirac cones coincides with the conventional one., 9 pages, 7 figures
- Published
- 2021
24. Plateau transitions of a spin pump and bulk-edge correspondence
- Author
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Yoshihito Kuno and Yasuhiro Hatsugai
- Subjects
Physics ,Condensed Matter - Materials Science ,Statistical Mechanics (cond-mat.stat-mech) ,Condensed matter physics ,Spins ,Materials Science (cond-mat.mtrl-sci) ,FOS: Physical sciences ,Plateau (mathematics) ,Magnetic field ,Quantum Gases (cond-mat.quant-gas) ,Condensed Matter::Strongly Correlated Electrons ,Valence bond theory ,Center of mass ,Boundary value problem ,Twist ,Condensed Matter - Quantum Gases ,Condensed Matter - Statistical Mechanics ,Spin-½ - Abstract
Sequential plateau transitions of quantum spin chains ($S$=1,3/2,2 and 3) are demonstrated by a spin pump using dimerization and staggered magnetic field as synthetic dimensions. The bulk is characterized by the Chern number associated with the boundary twist and the pump protocol as a time. It counts the number of critical points in the loop that is specified by the $Z_2$ Berry phases. With open boundary condition, discontinuity of the spin weighted center of mass due to emergent effective edge spins also characterizes the pump as the bulk edge correspondence. It requires extra level crossings in the pump as a super-selection rule that is consistent with the Valence Bond Solid (VBS) picture., 11 pages, 6 figures
- Published
- 2021
25. Edge states of a diffusion equation in one dimension: Rapid heat conduction to the heat bath
- Author
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Shusei Makino, Takahiro Fukui, Tsuneya Yoshida, and Yasuhiro Hatsugai
- Subjects
Condensed Matter - Mesoscale and Nanoscale Physics ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,FOS: Physical sciences - Abstract
We propose a one-dimensional (1D) diffusion equation (heat equation) for systems in which the diffusion constant (thermal diffusivity) varies alternately with a spatial period $a$. We solve the time evolution of the field (temperature) profile from a given initial distribution, by diagonalising the Hamiltonian, i.e., the Laplacian with alternating diffusion constants, and expanding the temperature profile by its eigenstates. We show that there are basically phases with or without edge states. The edge states affect the heat conduction around heat baths. In particular, rapid heat transfer to heat baths would be observed in a short time regime, which is estimated to be $t, 10 pages, 12 figures, v2: references added, text revised
- Published
- 2021
26. Correlation effects on non-Hermitian point-gap topology in zero dimension: reduction of topological classification
- Author
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Tsuneya Yoshida and Yasuhiro Hatsugai
- Subjects
Physics ,Quantum Physics ,Chern class ,Strongly Correlated Electrons (cond-mat.str-el) ,Statistical Mechanics (cond-mat.stat-mech) ,Condensed Matter - Mesoscale and Nanoscale Physics ,Degrees of freedom (physics and chemistry) ,FOS: Physical sciences ,Topology ,Hermitian matrix ,Condensed Matter - Strongly Correlated Electrons ,Zeroth law of thermodynamics ,Transition point ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Quantum Physics (quant-ph) ,Topology (chemistry) ,Condensed Matter - Statistical Mechanics ,Spin-½ ,Zero-dimensional space - Abstract
We analyze a zero-dimensional correlated system with special emphasis on the non-Hermitian point-gap topology protected by chiral symmetry. Our analysis elucidates that correlations destroy an exceptional point on a topological transition point which separates two topological phases in the non-interacting case; one of them is characterized by the zero-th Chern number $N_{0\mathrm{Ch}}=0$, and the other is characterized by $N_{0\mathrm{Ch}}=2$. This fact implies that correlations allow to continuously connect the two distinct topological phases in the non-interacting case without closing the point-gap, which is analogous to the reduction of topological classifications by correlations in Hermitian systems. Furthermore, we also discover a Mott exceptional point, an exceptional point where only spin degrees of freedom are involved., Revised version, 10 pages 9 figures
- Published
- 2021
27. Higher-Order Topological Mott Insulator on the Pyrochlore Lattice
- Author
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Seiji Yunoki, Koji Kudo, Yuichi Otsuka, Yasuhiro Hatsugai, and Tsuneya Yoshida
- Subjects
Physics ,Condensed Matter::Quantum Gases ,Multidisciplinary ,Strongly Correlated Electrons (cond-mat.str-el) ,Science ,Quantum Monte Carlo ,Mott insulator ,Quantum physics ,FOS: Physical sciences ,Order (ring theory) ,Topology ,Computer Science::Digital Libraries ,Article ,Condensed Matter - Strongly Correlated Electrons ,Gapless playback ,Topological insulator ,Phase (matter) ,Computer Science::Mathematical Software ,Medicine ,Topological order ,Condensed Matter::Strongly Correlated Electrons ,Condensed-matter physics ,Spin-½ - Abstract
We provide the first unbiased evidence for a higher-order topological Mott insulator in three dimensions by numerically exact quantum Monte Carlo simulations. This insulating phase is adiabatically connected to a third-order topological insulator in the noninteracting limit, which features gapless modes around the corners of the pyrochlore lattice and is characterized by a $\mathbb{Z}_{4}$ spin-Berry phase. The difference between the correlated and non-correlated topological phases is that in the former phase the gapless corner modes emerge only in spin excitations being Mott-like. We also show that the topological phase transition from the third-order topological Mott insulator to the usual Mott insulator occurs when the bulk spin gap solely closes., 10 pages, 9 figures
- Published
- 2021
28. Multiple quantum scar states and emergent slow-thermalization in the flat-band system
- Author
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Yasuhiro Hatsugai, Yoshihito Kuno, and Tomonari Mizoguchi
- Subjects
Physics ,Statistical Mechanics (cond-mat.stat-mech) ,Entropy (statistical thermodynamics) ,Degenerate energy levels ,FOS: Physical sciences ,Quantum entanglement ,State (functional analysis) ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Condensed Matter - Disordered Systems and Neural Networks ,Quantum mechanics ,Degeneracy (mathematics) ,Scaling ,Eigenstate thermalization hypothesis ,Quantum ,Condensed Matter - Statistical Mechanics - Abstract
Quantum many-body scars (QMBS) appear in a flat-band model with interactions on the saw-tooth lattice. The flat-band model includes a compact support localized eigenstates, called compact localized state (CLS). Some characteristic many-body states can be constructed from the CLSs at a low-filling on the flat-band. These many-body states are degenerate. Starting with such degenerate states we concretely show how to construct multiple QMBSs with different eigenenergies embedded in the entire spectrum. If the degeneracy is lifted by introducing hopping modulation or weak perturbations, these states lifted by these ways can be viewed as multiple QMBSs. In this work, we focus on the study of the perturbation-induced QMBS. Perturbed states, which are connected to the exact QMBSs in the unperturbed limit, indicate common properties of conventional QMBS systems, that is, a subspace with sub-volume or area law scaling entanglement entropy, which indicates the violation of the strong eigenstate thermalization hypothesis (ETH). Also for a specific initial state, slow-thermalization dynamics appears. We numerically demonstrate these subjects. The flat-band model with interactions is a characteristic example in non-integrable systems with the violation of the strong ETH and the QMBS., 13 pages, 9 figures
- Published
- 2021
29. Revisiting Flat bands and localization
- Author
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Yasuhiro Hatsugai
- Subjects
Physics ,Statistical Mechanics (cond-mat.stat-mech) ,Condensed matter physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,010308 nuclear & particles physics ,Zero (complex analysis) ,Pyrochlore ,FOS: Physical sciences ,General Physics and Astronomy ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Sawtooth wave ,engineering.material ,Condensed Matter - Disordered Systems and Neural Networks ,01 natural sciences ,Dimension (vector space) ,Lattice (order) ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,0103 physical sciences ,engineering ,Molecular orbital ,Condensed Matter::Strongly Correlated Electrons ,010306 general physics ,Degeneracy (mathematics) ,Randomness ,Condensed Matter - Statistical Mechanics - Abstract
Flat bands imply lack of itinerancy due to some constraints that, in principle, results in anomalous behaviors with randomness. By a molecular orbital (MO) representation of the flat band systems, random MO models are introduced where the degeneracy due to the flat bands is preserved even with randomness. The zero modes of the chiral symmetric system with sublattice imbalance belong to the class. After explaining the generic flat band construction by MOs, several examples are discussed with numerical demonstration as sawtooth lattice in one dimension and hyper-Pyrochlore lattice in any $d$-dimensions that extends the Kagome ($d=2$) and Pyrochlore ($d=3$) lattices to general dimensions., 12 pages, 3 figures, to appear in proceedings of Localisation 2020
- Published
- 2021
30. Square-root topological phase with time-reversal and particle-hole symmetry
- Author
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Yasuhiro Hatsugai, Tsuneya Yoshida, Tomonari Mizoguchi, and Yoshihito Kuno
- Subjects
Physics ,Toy model ,Condensed Matter - Mesoscale and Nanoscale Physics ,Phase (waves) ,FOS: Physical sciences ,02 engineering and technology ,Edge (geometry) ,021001 nanoscience & nanotechnology ,Topology ,01 natural sciences ,Symmetry (physics) ,Square root ,0103 physical sciences ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,010306 general physics ,0210 nano-technology ,Topology (chemistry) ,Hamiltonian (control theory) ,Surface states - Abstract
Square-root topological phases have been discussed mainly for systems with chiral symmetry. In this paper, we analyze the topology of the squared Hamiltonian for systems preserving the time-reversal and particle-hole symmetry. Our analysis elucidates that two-dimensional systems of class CII host helical edge states due to the nontrivial topology of the squared Hamiltonian in contrast to the absence of ordinary topological phases. The emergence of the helical edge modes is demonstrated by analyzing a toy model. We also show the emergence of surface states induced by the non-trivial topology of the squared Hamiltonian in three dimensions., Comment: 9 pages, 3 figures, references are added
- Published
- 2021
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- View/download PDF
31. Discriminant indicators with generalized inversion symmetry
- Author
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Tsuneya Yoshida, Ryo Okugawa, and Yasuhiro Hatsugai
- Subjects
Superconductivity (cond-mat.supr-con) ,Condensed Matter - Strongly Correlated Electrons ,Quantum Physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Statistical Mechanics (cond-mat.stat-mech) ,Strongly Correlated Electrons (cond-mat.str-el) ,Condensed Matter - Superconductivity ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,FOS: Physical sciences ,Quantum Physics (quant-ph) ,Condensed Matter - Statistical Mechanics - Abstract
We propose indicators of the discriminant for systems with generalized inversion symmetry which are computed from data only at high-symmetry points in the Brillouin zone. Our approach captures the exceptional points and their symmetry-protected variants without ambiguity arising from the reference energy, which is advantage over the previously known indicators for non-Hermitian systems. As demonstrations, we systematically analyze $3\times 3$-Hamiltonians where the proper choice of the reference energy is not obvious., Comment: 8 pages and 3 figures
- Published
- 2021
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32. Machine Learning Study on the Flat-Band States Constructed by Molecular-Orbital Representation with Randomness
- Author
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Takumi Kuroda, Tomonari Mizoguchi, Hiromu Araki, and Yasuhiro Hatsugai
- Subjects
Condensed Matter - Mesoscale and Nanoscale Physics ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,General Physics and Astronomy ,FOS: Physical sciences - Abstract
We study the characteristic probability density distribution of random flat band models by machine learning. The models considered here are constructed on the basis of the molecular-orbital representation, which guarantees the existence of the macroscopically degenerate zero-energy modes even in the presence of randomness. We find that flat band states are successfully distinguished from conventional extended and localized states, indicating the characteristic feature of the flat band states. We also find that the flat band states can be detected when the target data are defined in the different lattice from the training data, which implies the universal feature of the flat band states constructed by the molecular-orbital representation., Comment: 6 pages, 7 figures
- Published
- 2021
- Full Text
- View/download PDF
33. Topological band theory of a generalized eigenvalue problem with Hermitian matrices: Symmetry-protected exceptional rings with emergent symmetry
- Author
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Takuma Isobe, Tsuneya Yoshida, and Yasuhiro Hatsugai
- Subjects
Physics ,Quantum Physics ,Toy model ,Condensed Matter - Mesoscale and Nanoscale Physics ,FOS: Physical sciences ,Topology ,Hermitian matrix ,Symmetry (physics) ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Hyperbolic metamaterials ,Electronic band structure ,Dispersion (water waves) ,Quantum Physics (quant-ph) ,Eigendecomposition of a matrix ,Eigenvalues and eigenvectors ,Physics - Optics ,Optics (physics.optics) - Abstract
So far, topological band theory is discussed mainly for systems described by eigenvalue problems. Here, we develop a topological band theory described by a generalized eigenvalue problem (GEVP). Our analysis elucidates that non-Hermitian topological band structures may emerge for systems described by a GEVP with Hermitian matrices. The above result is verified by analyzing a two-dimensional toy model where symmetry-protected exceptional rings (SPERs) emerge although the matrices involved are Hermitian. Remarkably, these SPERs are protected by emergent symmetry, which is unique to the systems described by the GEVP. Furthermore, these SPERs elucidate the origin of the characteristic dispersion of hyperbolic metamaterials which is observed in experiments., Comment: 9 pages, 3 figures
- Published
- 2021
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- View/download PDF
34. Flat-band solutions in $D$-dimensional decorated diamond and pyrochlore lattices: Reduction to molecular problem
- Author
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Yasuhiro Hatsugai, Tomonari Mizoguchi, Isao Maruyama, and Hosho Katsura
- Subjects
Physics ,Condensed Matter - Materials Science ,Condensed matter physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Strongly Correlated Electrons (cond-mat.str-el) ,Pyrochlore ,Diamond ,Materials Science (cond-mat.mtrl-sci) ,FOS: Physical sciences ,Crystal structure ,engineering.material ,law.invention ,Condensed Matter - Strongly Correlated Electrons ,law ,Dispersion relation ,Line graph ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,engineering ,Variety (universal algebra) ,Wave function ,Realization (systems) - Abstract
Flat-band models have been of particular interest from both fundamental aspects and realization in materials. Beyond the canonical examples such as Lieb lattices and line graphs, a variety of tight-binding models are found to possess flat bands. However, analytical treatment of dispersion relations is limited, especially when there are multiple flat bands with different energies. In this paper, we present how to determine flat-band energies and wave functions in tight-binding models on decorated diamond and pyrochlore lattices in generic dimensions $D \geq 2$. For two and three dimensions, such lattice structures are relevant to various organic and inorganic materials, and thus our method will be useful to analyze the band structures of these materials., Comment: 13 pages, 10 figures
- Published
- 2021
- Full Text
- View/download PDF
35. Topological pump and bulk-edge-correspondence in an extended Bose-Hubbard model
- Author
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Yasuhiro Hatsugai and Yoshihito Kuno
- Subjects
Physics ,Optical lattice ,Strongly Correlated Electrons (cond-mat.str-el) ,Boundary (topology) ,FOS: Physical sciences ,Bose–Hubbard model ,Plateau (mathematics) ,Topology ,Condensed Matter - Strongly Correlated Electrons ,Grand canonical ensemble ,Geometric phase ,Quantum Gases (cond-mat.quant-gas) ,Topological order ,Condensed Matter - Quantum Gases ,Topology (chemistry) - Abstract
An extended Bose-Hubbard model (EBHM) with three- and four-body constraints can be feasible in cold atoms in an optical lattice. A rich phase structure including various symmetry-protected topological (SPT) phases is obtained numerically with suitable parameter settings and particle filling. The SPT phase is characterized by the Berry phase as a local topological order parameter and the structure of the entanglement spectrum (ES). Based on the presence of various topological phases, separated by gapless phase boundaries, the EBHM exhibits various bosonic topological pumps, which are constructed by connecting the different SPT phases without gap closing. The bulk topological pumps exhibit the plateau transitions characterized by many-body Chern numbers. For the system with boundary, the center of mass (CoM) under grand canonical ensemble elucidates the contributions of multiple edge states and reveals the topology of the system. We demonstrate that the interacting bosonic pumps obey the bulk-edge-correspondence., Comment: 12 pages, 6 figures
- Published
- 2021
- Full Text
- View/download PDF
36. Chiral edge modes in evolutionary game theory: a kagome network of rock-paper-scissors
- Author
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Yasuhiro Hatsugai, Tsuneya Yoshida, and Tomonari Mizoguchi
- Subjects
Physics ,Chern class ,Statistical Mechanics (cond-mat.stat-mech) ,Condensed Matter - Mesoscale and Nanoscale Physics ,Normal-form game ,Mode (statistics) ,FOS: Physical sciences ,Fermion ,Edge (geometry) ,Condensed Matter - Soft Condensed Matter ,Theoretical physics ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Soft Condensed Matter (cond-mat.soft) ,Quantitative Biology::Populations and Evolution ,Realization (systems) ,Quantum ,Topology (chemistry) ,Condensed Matter - Statistical Mechanics - Abstract
We theoretically demonstrate the realization of a chiral edge mode in a system beyond natural science. Specifically, we elucidate that a kagome network of rock-paper-scissors (K-RPS) hosts a chiral edge mode of the population density which is protected by the non-trivial topology in the bulk. The emergence of the chiral edge mode is demonstrated by numerically solving the Lotka-Volterra (LV) equation. This numerical result can be intuitively understood in terms of cyclic motion of a single RPS cycle which is analogues to the cyclotron motion of fermions. Furthermore, we point out that a linearized LV equation is mathematically equivalent to the Schr\"odinger equation describing quantum systems. This equivalence allows us to clarify the topological origin of the chiral edge mode in the K-RPS; a non-zero Chern number of the payoff matrix induces the chiral edge mode of the population density, which exemplifies the bulk-edge correspondence in two-dimensional systems described by evolutionary game theory., Comment: 7 pages, 7 figures
- Published
- 2020
37. Bulk-edge correspondence with generalized chiral symmetry
- Author
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Tohru Kawarabayashi and Yasuhiro Hatsugai
- Subjects
Physics ,Chiral symmetry ,Strongly Correlated Electrons (cond-mat.str-el) ,Condensed Matter - Mesoscale and Nanoscale Physics ,FOS: Physical sciences ,02 engineering and technology ,State (functional analysis) ,Edge (geometry) ,021001 nanoscience & nanotechnology ,01 natural sciences ,Condensed Matter - Strongly Correlated Electrons ,Critical mass ,Quantum mechanics ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,0103 physical sciences ,Wave vector ,Symmetry breaking ,Edge states ,010306 general physics ,0210 nano-technology - Abstract
The bulk-edge correspondence in topological phases is extended to systems with the generalized chiral symmetry, where the conventional chiral symmetry is broken. In such systems, we find that the edge state exhibits an unconventional behavior in the presence of the symmetry breaking by the mass, which is explored explicitly in the case of a deformed Su-Schrieffer-Heeger model. The localization length of the edge states diverges at a certain critical mass, where the edge state touches to the bulk band. The edge state is specified by an imaginary wave vector that becomes real at the touching energy., 11 pages, 9 figures
- Published
- 2020
38. Flat Band Quantum Scar
- Author
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Tomonari Mizoguchi, Yasuhiro Hatsugai, and Yoshihito Kuno
- Subjects
Crystal system ,FOS: Physical sciences ,02 engineering and technology ,Sawtooth wave ,01 natural sciences ,Condensed Matter - Strongly Correlated Electrons ,Quantum mechanics ,0103 physical sciences ,Energy spectrum ,010306 general physics ,Quantum ,Eigenstate thermalization hypothesis ,Eigenvalues and eigenvectors ,Condensed Matter - Statistical Mechanics ,Physics ,Condensed Matter - Materials Science ,Statistical Mechanics (cond-mat.stat-mech) ,Strongly Correlated Electrons (cond-mat.str-el) ,Materials Science (cond-mat.mtrl-sci) ,State (functional analysis) ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Condensed Matter - Disordered Systems and Neural Networks ,021001 nanoscience & nanotechnology ,Nonlinear Sciences::Chaotic Dynamics ,Quantum Gases (cond-mat.quant-gas) ,Flat band ,0210 nano-technology ,Condensed Matter - Quantum Gases - Abstract
We show that a quantum scar state, an atypical eigenstate breaking eigenstate thermalization hypothesis embedded in a many-body energy spectrum, can be constructed in flat band systems. The key idea of our construction is to make use of orthogonal compact localized states. We concretely discuss our construction scheme, taking a saw-tooth flat lattice system as an example, and numerically demonstrate the presence of a quantum scar state. Examples of higher-dimensional systems are also addressed. Our construction method of quantum scar has broad applications to various flat band systems., 5+2 pages, 3+4 figures
- Published
- 2020
39. Interaction induced doublons and embedded topological subspace in a complete flat-band system
- Author
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Tomonari Mizoguchi, Yasuhiro Hatsugai, and Yoshihito Kuno
- Subjects
Physics ,Statistical Mechanics (cond-mat.stat-mech) ,Strongly Correlated Electrons (cond-mat.str-el) ,Condensed Matter - Superconductivity ,Hilbert space ,FOS: Physical sciences ,Weak interaction ,Topology ,01 natural sciences ,010305 fluids & plasmas ,Superconductivity (cond-mat.supr-con) ,symbols.namesake ,Condensed Matter - Strongly Correlated Electrons ,Quantum Gases (cond-mat.quant-gas) ,0103 physical sciences ,Projection method ,symbols ,Quasiparticle ,Flat band ,010306 general physics ,Hamiltonian (quantum mechanics) ,Condensed Matter - Quantum Gases ,Subspace topology ,Condensed Matter - Statistical Mechanics - Abstract
In this work, we investigate effects of weak interactions on a bosonic complete flat-band system. By employing a band projection method, the flat-band Hamiltonian with weak interactions is mapped to an effective Hamiltonian. The effective Hamiltonian indicates that doublons behave as well-defined quasi-particles, which acquire itinerancy through the hopping induced by interactions. When we focus on a two-particle system, from the effective Hamiltonian, an effective subspace spanned only by doublon bases emerges. The effective subspace induces spreading of a single doublon and we find an interesting property: The dynamics of a single doublon keeps short-range density-density correlation in sharp contrast to a conventional two-particle spreading. Furthermore, when introducing a modulated weak interaction, we find an interaction induced topological subspace embedded in the full Hilbert space. We elucidate the embedded topological subspace by observing the dynamics of a single doublon, and show that the embedded topological subspace possesses a bulk topological invariant. We further expect that for the system with open boundary the embedded topological subspace has an interaction induced topological edge mode described by the doublon. The bulk--edge--correspondence holds even for the embedded topological subspace., 10 pages, 9 figures
- Published
- 2020
40. Bulk-edge correspondence of classical diffusion phenomena
- Author
-
Yasuhiro Hatsugai and Tsuneya Yoshida
- Subjects
Diffusion equation ,Field (physics) ,Science ,Crystal system ,FOS: Physical sciences ,Edge (geometry) ,Computer Science::Digital Libraries ,01 natural sciences ,Article ,010305 fluids & plasmas ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,0103 physical sciences ,Wavenumber ,Diffusion (business) ,010306 general physics ,Condensed-matter physics ,Condensed Matter - Statistical Mechanics ,Topological matter ,Physics ,Multidisciplinary ,Statistical Mechanics (cond-mat.stat-mech) ,Condensed matter physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Winding number ,Honeycomb (geometry) ,Condensed Matter - Other Condensed Matter ,Medicine ,Other Condensed Matter (cond-mat.other) - Abstract
We elucidate that the diffusive systems, which are widely found in nature, can be a new platform of the bulk-edge correspondence, a representative topological phenomenon. Using a discretized diffusion equation, we demonstrate the emergence of robust edge states protected by the winding number for one- and two-dimensional systems. These topological edge states can be experimentally accessible by measuring the diffusive dynamics at the edges. Furthermore, we discover a novel diffusive phenomenon by numerically simulating the distribution of temperatures for a honeycomb lattice system; the temperature field with wavenumber $\pi$ cannot diffuse to the bulk, which is attributed to the complete localization of the edge state., Comment: 9 pages, 7 figures, a reference is added, typos are corrected
- Published
- 2020
41. Detecting Bulk Topology of Quadrupolar Phase from Quench Dynamics
- Author
-
Yoshihito Kuno, Tomonari Mizoguchi, and Yasuhiro Hatsugai
- Subjects
Physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Numerical analysis ,Time evolution ,FOS: Physical sciences ,General Physics and Astronomy ,Observable ,Topology ,01 natural sciences ,Unitary state ,Quantum Gases (cond-mat.quant-gas) ,Phase (matter) ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,0103 physical sciences ,Quadrupole ,Condensed Matter - Quantum Gases ,010306 general physics ,Quantum ,Eigenvalues and eigenvectors ,Optics (physics.optics) ,Physics - Optics - Abstract
Direct measurement of a bulk topological observable in topological phase of matter has been a long-standing issue. Recently, detection of bulk topology through quench dynamics has attracted growing interests. Here, we propose that topological characters of a quantum quadrupole insulator can be read out by quench dynamics. Specifically, we introduce a quantity, a quadrupole moment weighted by the eigenvalues of the chiral operator, which takes zero for the trivial phase and finite for the quadrupolar topological phase. By utilizing an efficient numerical method to track the unitary time evolution, we elucidate that the quantity we propose indeed serves as an indicator of topological character for both noninteracting and interacting cases. The robustness against disorders is also demonstrated., 6 pages, 4 figures for the main text; 8 pages, 6 figures for Supplemental Material
- Published
- 2020
42. Exceptional band touching for strongly correlated systems in equilibrium
- Author
-
Robert Peters, Yasuhiro Hatsugai, Tsuneya Yoshida, and Norio Kawakami
- Subjects
Physics ,Quantum Physics ,Strongly Correlated Electrons (cond-mat.str-el) ,Condensed Matter - Mesoscale and Nanoscale Physics ,FOS: Physical sciences ,General Physics and Astronomy ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,02 engineering and technology ,Condensed Matter - Disordered Systems and Neural Networks ,021001 nanoscience & nanotechnology ,01 natural sciences ,Condensed Matter - Strongly Correlated Electrons ,Theoretical physics ,Perspective (geometry) ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,0103 physical sciences ,Quantum Physics (quant-ph) ,010306 general physics ,0210 nano-technology ,Quantum - Abstract
Quasi-particles described by Green's functions of equilibrium systems exhibit non-Hermitian topological phenomena because of their finite lifetime. This non-Hermitian perspective on equilibrium systems provides new insights into correlated systems and attracts much interest because of its potential to solve open questions in correlated compounds. In this paper, we provide a concise review of the non-Hermitian topological band structures for quantum many-body systems in equilibrium as well as their classification., 25 pages, 11 figures. Submitted to special section of Progress of Theoretical and Experimental Physics as an invited article
- Published
- 2020
43. Topological Modes Protected by Chiral and Two-Fold Rotational Symmetry in a Spring-Mass Model with a Lieb Lattice Structure
- Author
-
Tsuneya Yoshida, Tomonari Mizoguchi, Hiromasa Wakao, and Yasuhiro Hatsugai
- Subjects
Physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Rotation symmetry ,Rotational symmetry ,General Physics and Astronomy ,FOS: Physical sciences ,Fold (geology) ,Crystal structure ,Topology ,01 natural sciences ,010305 fluids & plasmas ,0103 physical sciences ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Quantum system ,010306 general physics - Abstract
We propose how to realize the topological modes, which correspond to topological zero modes for a quantum system, protected by chiral and rotation symmetry for a mechanical system. Specifically, we show the emergence of topological modes protected by chiral and two-fold rotational symmetry by a spring-mass system with a Lieb lattice structure and dents on the floor. Moreover, comparing the results of a tight-binding model, we have found the additional topological modes for our spring-mass model due to the extra degrees of freedoms. Our approach to realize the topological modes can be applied to other cases with rotation symmetry, e.g., a system of a honeycomb lattice with three-fold rotational symmetry., 4 pages, 2 figures
- Published
- 2020
44. Square-root higher-order topological insulator on a decorated honeycomb lattice
- Author
-
Tomonari Mizoguchi, Yasuhiro Hatsugai, and Yoshihito Kuno
- Subjects
Physics ,Condensed matter physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,FOS: Physical sciences ,01 natural sciences ,Square (algebra) ,010305 fluids & plasmas ,symbols.namesake ,Square root ,Topological insulator ,Lattice (order) ,0103 physical sciences ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,symbols ,010306 general physics ,Hamiltonian (quantum mechanics) ,Photonic crystal ,Bloch wave ,Optics (physics.optics) ,Physics - Optics - Abstract
Square-root topological insulators are recently-proposed intriguing topological insulators, where the topologically nontrivial nature of Bloch wave functions is inherited from the square of the Hamiltonian. In this paper, we propose that higher-order topological insulators can also have their square-root descendants, which we term square-root higher-order topological insulators. There, emergence of in-gap corner states is inherited from the squared Hamiltonian which hosts higher-order topology. As an example of such systems, we investigate the tight-binding model on a decorated honeycomb lattice, whose squared Hamiltonian includes a breathing kagome-lattice model, a well-known example of higher-order topological insulators. We show that the in-gap corner states appear at finite energies, which coincides with the non-trivial bulk polarization. We further show that the existence of in-gap corner states results in characteristic single-particle dynamics, namely, setting the initial state to be localized at the corner, the particle stays at the corner even after a long time. Such characteristic dynamics may experimentally be detectable in photonic crystals., 8 pages, 5 figures for main text; 1 page, 1 figure for erratum. v3: Erratum is incorporated [Phys. Rev. A 104, 029906 (2021)]
- Published
- 2020
45. Higher-order topological phases in a spring-mass model on a breathing kagome lattice
- Author
-
Hiromasa Wakao, Hiromu Araki, Tomonari Mizoguchi, Yasuhiro Hatsugai, and Tsuneya Yoshida
- Subjects
Physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Lattice (group) ,FOS: Physical sciences ,Order (ring theory) ,02 engineering and technology ,State (functional analysis) ,021001 nanoscience & nanotechnology ,Coupling (probability) ,Topology ,01 natural sciences ,Brillouin zone ,Geometric phase ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,0103 physical sciences ,Boundary value problem ,010306 general physics ,0210 nano-technology ,Realization (systems) - Abstract
We propose a realization of higher-order topological phases in a spring-mass model with a breathing kagome structure. To demonstrate the existence of the higher-order topological phases, we characterize the topological properties and show that the corner states appear under the fixed boundary condition. To characterize the topological properties, we introduce a formula for the $\mathbb{Z}_3$ Berry phases in the Brillouin zone. From the numerical result of this $\mathbb{Z}_3$ Berry phase, we have elucidated that coupling between the longitudinal and transverse modes yields a state characterized by the Berry phase $\frac{2\pi}{3}$ for our mechanical breathing kagome model. In addition, we suggest that the corner states can be detected experimentally through a forced vibration., Comment: 9 pages, 10 figures
- Published
- 2020
46. Systematic construction of topological flat-band models by molecular-orbital representation
- Author
-
Yasuhiro Hatsugai and Tomonari Mizoguchi
- Subjects
Physics ,Class (set theory) ,Strongly Correlated Electrons (cond-mat.str-el) ,Basis (linear algebra) ,Condensed Matter - Mesoscale and Nanoscale Physics ,FOS: Physical sciences ,02 engineering and technology ,Construct (python library) ,021001 nanoscience & nanotechnology ,Topology ,01 natural sciences ,Condensed Matter - Strongly Correlated Electrons ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,0103 physical sciences ,Molecular orbital ,Flat band ,010306 general physics ,0210 nano-technology ,Electronic band structure ,Representation (mathematics) ,Topology (chemistry) - Abstract
On the basis of the "molecular-orbital" representation which describes generic flat-band models, we propose a systematic way to construct a class of flat-band models with finite-range hoppings that have topological natures. In these models, the topological natures are encoded not into the flat band itself but into the dispersive bands touching the flat band. Such a band structure may become a source of exotic phenomena arising from the combination of flat bands, topology and correlations., 9 pages, 7 figures
- Published
- 2020
47. ZQ Berry phase for higher-order symmetry-protected topological phases
- Author
-
Tomonari Mizoguchi, Hiromu Araki, and Yasuhiro Hatsugai
- Subjects
Physics ,Geometric phase ,Order (ring theory) ,Invariant (mathematics) ,Topology ,Spin (physics) ,Symmetry (physics) - Abstract
The authors propose that the quantized Berry phase serves as a many-body topological invariant that characterizes the higher-order symmetry-protected topological phases in two- and three-dimensions, and provides a clear insight of bulk-corner correspondence. The quantized Berry phase has wide applicability ranging from fermionic models with and without interactions to spin models.
- Published
- 2020
48. Adiabatic Heuristic Principle on a Torus and Generalized Streda Formula
- Author
-
Yasuhiro Hatsugai and Koji Kudo
- Subjects
Physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Strongly Correlated Electrons (cond-mat.str-el) ,Topological degeneracy ,Anyon ,FOS: Physical sciences ,Torus ,Topological quantum computer ,Condensed Matter - Strongly Correlated Electrons ,High Energy Physics::Theory ,Adiabatic invariant ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Degeneracy (mathematics) ,Heuristic argument ,Adiabatic process ,Mathematical physics - Abstract
Although the adiabatic heuristic argument of the fractional quantum Hall states has been successful, continuous modification of the flux/statistics of anyons is strictly prohibited due to algebraic constrains of the braid group on a torus. We have numerically shown that the adiabatic heuristic principle for anyons is still valid even though the Hamiltonians cannot be modified continuously. The Chern number of the ground state multiplet is the adiabatic invariant, while the number of the topological degeneracy behaves wildly. A generalized Streda formula is proposed that explains the degeneracy pattern. Nambu-Goldston modes associated with the anyon superconductivity are also suggested numerically., Comment: 7 pages
- Published
- 2020
- Full Text
- View/download PDF
49. Type-III Dirac Cones from Degenerate Directionally Flat Bands: Viewpoint from Molecular-Orbital Representation
- Author
-
Tomonari Mizoguchi and Yasuhiro Hatsugai
- Subjects
Physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Dirac (software) ,Degenerate energy levels ,Representation (systemics) ,General Physics and Astronomy ,FOS: Physical sciences ,Type (model theory) ,01 natural sciences ,010305 fluids & plasmas ,Quantum mechanics ,0103 physical sciences ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Molecular orbital ,Flat band ,010306 general physics - Abstract
We present a systematic method of creating type-III Dirac cones from degenerate directionally flat bands. Here, the directionally flat band means a completely dispersionless band only in a certain direction. The key strategy is to retain one of the directionally flat bands while making the other dispersive, by adding a perturbation having a selected form of a Hamiltonian matrix. Such a form of a perturbation is found by using the "molecular-orbital representation" which we have developed to describe flat-band models. The models thus obtained host type-III Dirac cones even without fine-tuning hopping parameters. To demonstrate the ubiquity of this method, we study concrete examples of two-band models and a four-band model., Comment: 5 pages, 4 figures
- Published
- 2020
- Full Text
- View/download PDF
50. Fate of fractional quantum Hall states in open quantum systems: characterization of correlated topological states for the full Liouvillian
- Author
-
Koji Kudo, Hosho Katsura, Yasuhiro Hatsugai, and Tsuneya Yoshida
- Subjects
Physics ,Quantum Physics ,Chern class ,Condensed Matter - Mesoscale and Nanoscale Physics ,Statistical Mechanics (cond-mat.stat-mech) ,Strongly Correlated Electrons (cond-mat.str-el) ,Hilbert space ,FOS: Physical sciences ,Characterization (mathematics) ,Quantum Hall effect ,Topology ,Linear subspace ,Condensed Matter - Strongly Correlated Electrons ,symbols.namesake ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,symbols ,Boundary value problem ,Quantum Physics (quant-ph) ,Quantum ,Condensed Matter - Statistical Mechanics - Abstract
Despite previous extensive analysis of open quantum systems described by the Lindblad equation, it is unclear whether correlated topological states, such as fractional quantum Hall states, are maintained even in the presence of the jump term. In this paper, we introduce the pseudo-spin Chern number of the Liouvillian which is computed by twisting the boundary conditions only for one of the subspaces of the doubled Hilbert space. The existence of such a topological invariant elucidates that the topological properties remain unchanged even in the presence of the jump term which does not close the gap of the effective non-Hermitian Hamiltonian (obtained by neglecting the jump term). In other words, the topological properties are encoded into an effective non-Hermitian Hamiltonian rather than the full Liouvillian. This is particularly useful when the jump term can be written as a strictly block-upper (-lower) triangular matrix in the doubled Hilbert space, in which case the presence or absence of the jump term does not affect the spectrum of the Liouvillian. With the pseudo-spin Chern number, we address the characterization of fractional quantum Hall states with two-body loss but without gain, elucidating that the topology of the non-Hermitian fractional quantum Hall states is preserved even in the presence of the jump term. This numerical result also supports the use of the non-Hermitian Hamiltonian which significantly reduces the numerical cost. Similar topological invariants can be extended to treat correlated topological states for other spatial dimensions and symmetry (e.g., one-dimensional open quantum systems with inversion symmetry), indicating the high versatility of our approach., Comment: 16 pages, 4figures, (to appear in Phys. Rev. Research)
- Published
- 2020
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