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We propose a generalization of the coherent anomaly method to extract the critical exponents of a phase transition occurring in the steady-state of an open quantum many-body system. The method, originally developed by Suzuki [J. Phys. Soc. Jpn. {\bf 55}, 4205 (1986)] for equilibrium systems, is based on the scaling properties of the singularity in the response functions determined through cluster mean-field calculations. We apply this method to the dissipative transverse-field Ising model and the dissipative XYZ model in two dimensions obtaining convergent results already with small clusters., Accepted version, 9 pages, 7 figures

We show that the onset of quantum chaos at infinite temperature in two many-body one-dimensional lattice models, the perturbed spin-1/2 XXZ and Anderson models, is characterized by universal behavior. Specifically, we show that the onset of quantum chaos is marked by maxima of the typical fidelity susceptibilities that scale with the square of the inverse average level spacing, saturating their upper bound, and that the strength of the integrability- or localization-breaking perturbation at these maxima decreases with increasing system size. We also show that the spectral function below the ``Thouless'' energy (in the quantum-chaotic regime) diverges when approaching those maxima. Our results suggest that, in the thermodynamic limit, arbitrarily small integrability- or localization-breaking perturbations result in quantum chaos in the many-body quantum systems studied here., 12 pages, 13 figures, as published

Spin carriers propagating along quantum circuits gather quantum spin phases depending on the circuit's size, shape, and spin-orbit coupling (SOC) strength. These phases typically grow monotonically with the SOC strength, as found in Rashba quantum wires and rings. In this work we show that the spin-phase gathering can be engineered by geometric means, viz. by the geometric curvature of the circuits, to be non-monotonic. We demonstrate this peculiar property by using one-dimensional polygonal models where flat segments alternate with highly curved vertices. The complex interplay between dynamic and geometric spin-phase components -- triggered by a series of emergent spin degeneracy points -- leads to bounded, global spin phases. Moreover, we show that the particulars of the spin-phase gathering have observable consequences in the Aharonov-Casher conductance of Rashba loops, a connection that passed unnoticed in previous works., Accepted version. 11 pages, 8 figures, 3 appendices

Recent experiments have discovered multipolar orders in a variety of $d$-orbital Mott insulators. Motivated by uncovering the exchange interactions which underlie octupolar order proposed in the osmate double perovskites, we study a two-site model using exact diagonalization on a five-orbital Hamiltonian, incorporating spin-orbit coupling (SOC) and interactions, and including both intra-orbital and inter-orbital hopping. Using an exact Schrieffer-Wolff transformation, we then extract an effective pseudospin Hamiltonian for the non-Kramers doublets, uncovering dominant ferrooctupolar coupling driven by the interplay of two distinct intra-orbital hopping terms. Using classical Monte Carlo simulations on the face-centered cubic lattice, we obtain a ferrooctupolar transition temperature which is in good agreement with experiments on the osmate double perovskites. We also explore the impact of uniaxial strain and dimensional tuning via ultrathin films, which are shown to induce a transverse field on the Ising octupolar order. This suppresses $T_c$ and potentially allows one to access octupolar Ising quantum critical points. We discuss possible implications of our results for a broader class of materials which may host such non-Kramers doublet ions., 11 pages, 8 figures

The spectral and temporal response of a set of $N$ quantum emitters embedded in a photonic cavity is studied. Quantum mechanically, such systems can be described by the Tavis-Cummings (TC) model of $N$ two-level systems coupled to a single light mode. Here we compare the full quantum solution of the TC model for different numbers of quantum emitters with its semiclassical limit after a pulsed excitation of the cavity mode. Considering different pulse amplitudes, we find that the spectra obtained from the TC model approach the semiclassical one for an increasing number of emitters $N$. Furthermore they match very well for small pulse amplitudes. While we observe a very good agreement in the temporal dynamics for photon numbers much smaller than $N$, considerable deviations occur in the regime of photon numbers similar to or larger than $N$, which are linked to collapse and revival phenomena. Wigner functions of the light mode are calculated for different scenarios to analyze the quantum state of the light field. We find strong deviations from a coherent state even if the dynamics of the expectation values are still well described by the semiclassical limit. For higher pulse amplitudes Wigner functions similar to those of Schr\"odinger cat states between two or more quasi-coherent contributions build up., Comment: accepted for publication in Physical Review B https://journals.aps.org/prb/

The operators of localized spins within a magnetic material commute at different sites of its lattice and anticommute on the same site, so they are neither fermionic nor bosonic operators. Thus, to construct diagrammatic many-body perturbation theory, the spin operators are usually mapped to the bosonic ones with Holstein-Primakoff (HP) transformation being the most widely used in magnonics and spintronics literature. However, to make calculations tractable, the square root of operators in the HP transformation is expanded into a Taylor series truncated to some low order. This poses a question on the range of validity of truncated HP transformation when describing nonequilibrium dynamics of localized spins interacting with each other or with conduction electron spins. Here we apply exact diagonalization techniques to Hamiltonian of fermions (i.e., electrons) interacting with HP bosons vs. Hamiltonian of fermions interacting with the original localized spin operators in order to compare their many-body states and one-particle equilibrium or nonequilibrium Green functions. The Hamiltonian of fermions interacting with HP bosons gives incorrect ground state and electronic spectral function, unless large number of terms are retained in truncated HP transformation. Furthermore, tracking nonequilibrium dynamics of localized spins over longer time intervals requires progressively larger number of terms in truncated HP transformation. Finally, we show that recently proposed [M. Vogl et al., Phys. Rev. Research 2, 043243 (2020); J. K\"{o}nig et al., SciPost Phys. 10, 007 (2021)] resummed HP transformation resolves the trouble with truncated HP transformation, while allowing us to derive an exact (manifestly Hermitian) Hamiltonian consisting of finite and fixed number of boson-boson and electron-boson interacting terms., Comment: 23 pages, 10 figures

We investigate the low-energy physics of non-Hermitian quantum spin models with $PT$-symmetry. To this end we consider the one-dimensional Ising chain and the two-dimensional toric code in a non-Hermitian staggered field. For both systems dual descriptions in terms of non-Hermitian staggered Ising interactions in a conventional transverse field exist. We perform high-order series expansions about the high- and low-field limit for both systems to determine the ground-state energy per site and the one-particle gap. The one-dimensional non-Hermitian Ising chain is known to be exactly solvable. Its ground-state phase diagram consists of second-order quantum phase transitions, which can be characterized by logarithmic singularities of the second derivative of the ground-state energy and, in the symmetry-broken phase, the gap closing of the low-field gap. In contrast, the gap closing from the high-field phase is not accessible perturbatively due to the complex energy and the occurrence of exceptional lines in the high-field gap expression. For the two-dimensional toric code in a non-Hermitian staggered field we study the quantum robustness of the topologically ordered phase by the gap closing of the low-field gap. We find that the well-known second-order quantum phase transition of the toric code in a uniform field extends into a large portion of the non-Hermitian parameter space. However, the series expansions become unreliable for a dominant anti-Hermitian field. Interestingly, the analysis of the high-field gap reveals the potential presence of an intermediate region., Comment: 15 pages, 9 figures

We propose an effect called information constraint which is characterized by the existence of different decay rates of signal strengths propagating along opposite directions. It is an intrinsic property of a type of open quantum system, which does not rely on boundary conditions. We define the value of information constraint ($I_C$) as the ratio of different decay rates and derive the analytical representation of $I_C$ for general quadratic Lindbladian systems. Based on information constraint, we can provide a simple and elegant explanation of chiral and helical damping, and get the local maximum points of relative particle number for the periodical boundary system, consistent with numerical calculations. Inspired by information constraint, we propose and prove the correspondence between edge modes and damping modes. A new damping mode called Dirac damping is constructed, and chiral/helical damping can be regarded as a special case of Dirac damping., 17 pages, 2 figures

We study the prethermalization and thermalization dynamics of local observables in weakly perturbed nonintegrable systems, with Hamiltonians of the form $\hat{H}_0+g\hat{V}$, where $\hat{H}_0$ is nonintegrable and $g\hat{V}$ is a perturbation. We explore the dynamics of far from equilibrium initial states in the thermodynamic limit using a numerical linked cluster expansion (NLCE), and in finite systems with periodic boundaries using exact diagonalization. We argue that generic observables exhibit a two-step relaxation process, with a fast prethermal dynamics followed by a slow thermalizing one, only if the perturbation breaks a conserved quantity of $\hat{H}_0$ and if the value of the conserved quantity in the initial state is $\mathcal{O}(1)$ different from the one after thermalization. We show that the slow thermalizing dynamics is characterized by a rate $\propto g^2$, which can be accurately determined using a Fermi golden rule (FGR) equation. We also show that during such a slow dynamics, observables can be described using projected diagonal and Gibbs ensembles, and we contrast their accuracy., 15 pages, 9 figures

We present an experimental and simulation study of the collective dynamics of liquid D2 in the range of exchanged wave vectors 3< Q< 14 nm-1. Neutron Brillouin scattering results for the center-of-mass dynamic structure factor of this moderately quantum fluid are compared, on an absolute scale, with those obtained by three different quantum simulation methods such as ring polymer molecular dynamics and two versions of the Feynman-Kleinert approach. The experimental data can be well described by dynamical models typically used for liquids. Some discrepancies show up both among simulations, and between simulations and experimental data. Such discrepancies are found to mainly concern the damping of the propagating sound modes.

For a large class of quantum many-body systems with U(1) symmetry, we prove a general inequality that relates the (off-diagonal) long-range order with the charge gap. For a system of bosons or fermions on a lattice or in the continuum, the inequality implies that a ground state with off-diagonal long-range order inevitably has a vanishing charge gap, and hence is characterized by nonzero charge susceptibility. For a quantum spin system, the inequality implies that a ground state within a magnetization plateau cannot have transverse long-range order., Comment: 10 pages, no figures. Minor imporvments in versions 2 and 3. There is a 16 minutes video in which the main results of the paper are described. See https://youtu.be/fvZdgV8Ik-8

A series of recent experiments have demonstrated robust superconductivity in magic-angle twisted trilayer graphene (TTG). In particular, a recent work by Cao et al. (arxiv:2103.12083) studies the behavior of the superconductor in an in-plane magnetic field and out-of-plane displacement field, finding that the superconductor is unlikely to be spin-singlet. This work also finds that at high magnetic fields and a smaller range of dopings and displacement fields, it undergoes a transition to a distinct field-induced superconducting state. Inspired by these results, we develop an understanding of superconductivity in TTG using a combination of phenomenological reasoning and microscopic theory. We describe role that that an in-plane field plays in TTG, and use this understanding to argue that the re-entrant transition may be associated with a quantum Lifshitz phase transition, with the high-field phase possessing finite-momentum pairing. We argue that the superconductor is likely to involve a superposition of singlet singlet and triplet pairing, and describe the structure of the normal state. We also draw lessons for twisted bilayer graphene (TBG), and explain the differences in the phenomenology with TTG despite their close microscopic relationship. We propose that a singlet-triplet superposition is realized in the TBG superconductor as well, and that the $\nu = -2$ correlated insulator may be a time reversal protected $\mathbb{Z}_2$ topological insulator obtained through spontaneous spin symmetry breaking., Comment: 7+21 pages. v2: added discussion on lessons for TBG v3: minor edits

The concept of free fermion topology has been generalized to $d$-dimensional phases that exhibit $(d-n)$-dimensional boundary modes, such as zero-dimensional (0D) corner excitations. Motivated by recent extensions of these ideas to magnetic systems, we consider 2D quantum paramagnets formed by interacting spin dimers with dispersive triplet excitations. We propose two examples of such dimer models, where the spin-gapped bosonic triplon excitations are shown to host bands with nontrivial higher-order topology. We demonstrate this using real-space Bogoliubov--de Gennes calculations that reveal the existence of mid-bandgap corner triplon modes as a signature of higher-order bulk topology. We provide an understanding of the higher-order topology in these systems via a computation of bulk topological invariants as well as the construction of edge theories, and study their phase transitions as we tune parameters in the model Hamiltonians. We also discuss possible experimental approaches for detecting the emergent corner triplon modes., 20 pages, 4 figures

The bulk electric polarization works as a nonlocal order parameter that characterizes topological quantum matters. Motivated by a recent paper [H. Watanabe \textit{et al.}, Phys. Rev. B {\bf 103}, 134430 (2021)], we discuss magnetic analogs of the bulk polarization in one-dimensional quantum spin systems, that is, quantized magnetizations on the edges of one-dimensional quantum spin systems.The edge magnetization shares the topological origin with the fractional edge state of the topological odd-spin Haldane phases. Despite this topological origin, the edge magnetization can also appear in topologically trivial quantum phases. We develop straightforward field theoretical arguments that explain the characteristic properties of the edge magnetization. The field theory shows that a U(1) spin-rotation symmetry and a site-centered or bond-centered inversion symmetry protect the quantization of the edge magnetization. We proceed to discussions that quantum phases on nonzero magnetization plateaus can also have the quantized edge magnetization that deviates from the magnetization density in bulk. We demonstrate that the quantized edge magnetization distinguishes two quantum phases on a magnetization plateau separated by a quantum critical point. The edge magnetization exhibits an abrupt stepwise change from zero to $1/2$ at the quantum critical point because the quantum phase transition occurs in the presence of the symmetries protecting the quantization of the edge magnetization. We also show that the quantized edge magnetization can result from the spontaneous ferrimagnetic order.

We analyze fermions after an interaction quantum quench in one spatial dimension and study the growth of the steady state entanglement entropy density under either a spatial mode or particle bipartition. For integrable lattice models, we find excellent agreement between the increase of spatial and particle entanglement entropy, and for chaotic models, an examination of two further neighbor interaction strengths suggests similar correspondence. This result highlights the generality of the dynamical conversion of entanglement to thermodynamic entropy under time evolution that underlies our current framework of quantum statistical mechanics., 11 pages. Now includes analysis of next-nearest-neighbor interactions. Updated code and data repository see, https://github.com/DelMaestroGroup/papers-code-EntanglementQuantumQuench

Giant optical circular birefringence (GCB) induced by a single quantum-dot-confined spin in an optical microcavity finds wide applications in quantum and optical technologies, such as quantum gates, quantum transistors, quantum repeaters, quantum routers, etc. If the system is probed with a classical light, such as the laser light where the photons are uncorrelated with each other, then the single-photon GCB is detected. In this work we develop a general approach to investigate the many-body dynamics of $n$ photons bound to one quantum emitter and apply this method to calculate the $n$-photon GCB probed with quantum light in Fock states. With suppressed atomic saturation, quantum light loads photons into dressed states more efficiently than classical light such that the whole Jaynes-Cummings energy ladder and the quantum nonlinearity related to the multiphoton transitions can be observed. The $n$-photon GCB lying at the cavity mode resonance allows the spin-cavity quantum gates and quantum transistors to extend from single-photon to $n$-photon operations and generate entangled photonic Fock states, i.e., the NOON states which are useful for quantum metrology and lithography.

Different channels over which electrons scatter between parts of the Fermi surface are the key to various electronic quantum matters, such as superconductivity and density waves. We consider an effective model in higher dimensions where each of the two pockets in the original model maps to (the Landau levels of) two Dirac fermions. We discover an emergent channel when two Dirac fermions from different pairs annihilate, where the presence of a strong density wave is essential. We support our analysis with numerical calculations on model examples in the vicinity of ferromagnetic and antiferromagnetic orders. We also discuss interesting consequences on electron interaction channels that beyond-mean-field fluctuations may induce., 6 pages, 7 figures

We study the Josephson effect in spin-triplet superconductor\ensuremath{-}quantum anomalous Hall insulator\ensuremath{-}spin-triplet superconductor junctions using the nonequilibrium Green's function method. The current-phase difference relations show strong dependence on the orientations of the $\mathbf{d}$ vectors in superconductors. We focus on two $\mathbf{d}$-vector configurations, a parallel one with the left and right $\mathbf{d}$ vectors being in the same direction and a nonparallel one with the left $\mathbf{d}$ vector fixed at the $z$ axis. For the parallel configuration, the $0\text{\ensuremath{-}}\ensuremath{\pi}$ transition can be realized when one rotates the $\mathbf{d}$ vectors from the parallel to the junction plane to the perpendicular direction. The ${\ensuremath{\phi}}_{0}$ phase with nonzero Josephson current at zero phase difference can be obtained as long as ${d}_{x}{d}_{z}\ensuremath{\ne}0$. For the nonparallel configuration, the $0\text{\ensuremath{-}}\ensuremath{\pi}$ transition and the ${\ensuremath{\phi}}_{0}$ phase still exist. The condition for the formation of the ${\ensuremath{\phi}}_{0}$ phase becomes ${d}_{Rx}\ensuremath{\ne}0$. The switch effects of the Josephson current are found in both configurations when the $\mathbf{d}$ vectors are rotated in the $xy$ plane. Furthermore, the symmetries satisfied by the current-phase difference relations are analyzed in detail by the operations of the time-reversal, mirror-reflections, the spin-rotation, and the gauge transformation, which can well explain the above selection rules for the ${\ensuremath{\phi}}_{0}$ phase. Our results reveal the peculiar Josephson effect between spin-triplet superconductors and the quantum anomalous Hall insulator, which provide helpful phases and effects for device designs. The distinct current-phase difference relations for different orientations may be used to determine the direction of the $\mathbf{d}$ vector in the spin-triplet superconductor.

The dynamics of arbitrary-order quantum correlations in a cavity magnon-polariton system are investigated based on the quantum master equation in the coherent state representation. The phenomena of Rabi-like oscillation and level repulsion of the average cavity-photon number agree remarkably well with existing experimental observations. The competing nature of coherent and incoherent components in these two cases is further revealed by the second-order quantum coherence of the cavity photons and magnons, which can be systematically tuned by the driving microwave and thermal bath. Our results demonstrate the rich higher-order quantum dynamics induced by magnetic light-matter interaction, and serve as an indispensable step toward exploring nonclassical states for cavity photons and magnons in quantum cavity magnonics., 11 pages, 6 figures

We add quantum fluctuations to a classical period-doubling Hamiltonian time crystal, replacing the $N$ classical interacting angular momenta with quantum spins of size $l$. The full permutation symmetry of the Hamiltonian allows a mapping to a bosonic model and the application of exact diagonalization for a quite large system size. In the thermodynamic limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$ the model is described by a system of Gross-Pitaevskii equations whose classical-chaos properties closely mirror the finite-$N$ quantum chaos. For $N\ensuremath{\rightarrow}\ensuremath{\infty}$, and $l$ finite, Rabi oscillations mark the absence of persistent period doubling, which is recovered for $l\ensuremath{\rightarrow}\ensuremath{\infty}$ with Rabi-oscillation frequency tending exponentially to 0. For the chosen initial conditions, we can represent this model in terms of Pauli matrices and apply the discrete truncated Wigner approximation. For finite $l$ this approximation reproduces no Rabi oscillations but correctly predicts the absence of period doubling. Our results show the instability of time-translation symmetry breaking in this classical system even to the smallest quantum fluctuations, because of tunneling effects.

The properties of mobile impurities in quantum magnets are fundamental for our understanding of strongly correlated materials and may play a key role in the physics of high-temperature superconductivity. Hereby, the motion of hole-like defects through an antiferromagnet has been of particular importance. It creates magnetic frustrations that lead to the formation of a quasiparticle, whose complex structure continues to pose substantial challenges to theory and numerical simulations. In this article, we develop a non-perturbative theoretical approach to describe the microscopic properties of such magnetic polarons. Based on the self-consistent Born approximation, which is provenly accurate in the strong-coupling regime, we obtain a complete description of the polaron wave function by solving a set of Dyson-like equations that permit to compute relevant spin-hole correlation functions. We apply this new method to analyze the spatial structure of magnetic polarons in the strongly interacting regime and find qualitative differences from predictions of previously applied truncation schemes. Our calculations reveal a remarkably high spatial symmetry of the polaronic magnetization cloud and a surprising misalignment between its orientation and the polaron crystal momentum. The developed framework opens up an approach to the microscopic properties of doped quantum magnets and will enable detailed analyses of ongoing experiments based on cold-atom quantum simulations of the Fermi-Hubbard model., 18 pages, 12 figures

In this work, we propose and study a one-dimensional model of the effects of optical phonon/magnon coupling. The indirect interactions between magnetic ions are conducted by the sandwiched nonmagnetic ions. The vibrations of nonmagnetic ions invoke effective magnetic fields to spins and hence couple with the magnon. The quantum solutions of the model show energy gaps in the spin-wave dispersion induced by the magnon-phonon coupling. Classical simulations reveal the existence of hybrid magnon-phonon quasiparticles and the coherent phonon (magnon) induced by magnon (phonon).

Funding Information: We thank L. Liang and M. Iskin for useful discussions. A.J. and P.T. acknowledge support by the Academy of Finland under Projects No. 303351, No. 307419, and No. 327293. A.J. acknowledges financial support from the Jenny and Antti Wihuri Foundation. This research was supported in part by the National Science Foundation under Grant No. PHY-1748958. We thank A. Paraoanu for producing the illustrations for Fig. . Publisher Copyright: © 2021 American Physical Society. The quantum geometry of Bloch states fundamentally affects a wide range of physical phenomena. The quantum Hall effect, for example, is governed by the Chern number, and flat-band superconductivity by the distance between the Bloch states: The quantum metric. While understanding quantum geometry phenomena in the context of fermions is well established, less is known about the role of quantum geometry in bosonic systems where particles can undergo Bose-Einstein condensation (BEC). In conventional single-band or continuum systems, excitations of a weakly interacting BEC are determined by the condensate density and the interparticle interaction energy. In contrast to this, we discover here fundamental connections between the properties of a weakly interacting BEC and the underlying quantum geometry of a multiband lattice system. We show that, in the flat-band limit, the defining physical quantities of BEC, namely, the speed of sound and the quantum depletion, are dictated solely by the quantum geometry. We find that the speed of sound becomes proportional to the quantum metric of the condensed state. Furthermore, the quantum distance between the Bloch functions forces the quantum depletion and the quantum fluctuations of the density-density correlation to obtain finite values for infinitesimally small interactions. This is in striking contrast to dispersive bands where these quantities vanish with the interaction strength. Additionally, we show how in the flat-band limit the supercurrent is carried by the quantum fluctuations and is determined by the Berry connections of the Bloch states. Our results reveal how nontrivial quantum geometry allows reaching strong quantum correlation regime of condensed bosons even with weak interactions. This is highly relevant, for example, for polariton and photon BECs where interparticle interactions are inherently small. Our predictions can be experimentally tested with flat-band lattices already implemented in ultracold gases and various photonic platforms.

We study a class of off-diagonal quasiperiodic hopping models described by a one-dimensional Su-Schrieffer-Heeger chain with quasiperiodic modulations. With regard to these models, we unveil a general dual-mapping relation in parameter space of the dimerization strength $\ensuremath{\lambda}$ and the quasiperiodic modulation strength $V$, regardless of specific details of quasiperiodic modulations. Moreover, we demonstrated semianalytically and numerically that under the specific quasiperiodic modulation, quantum criticality, namely the criticality of wave functions, can emerge and persist in a wide parameter space. These unusual results provide a distinctive paradigm compared with the diagonal quasiperiodic systems and perspectives for future investigations on quasiperiodic disorder.

The discovery of the Berezinskii-Kosterlitz-Thouless transition some fifty years ago was a subject of the 2016 Nobel Prize in Physics. However, quantitative study of the transition in the two-dimensional XY spin model still suffers from significant finite-size effects. The authors implement the level-spectroscopy method, originally developed for quantum systems. They utilize the modern tensor-network renormalization scheme. This allows for an extremely accurate determination of the critical point as well as for a visualization of the celebrated Kosterlitz renormalization-group flow.

Characterizing the many-body localization (MBL) transition in strongly disordered and interacting quantum systems is an important issue in the field of condensed matter physics. We study the single particle Green's functions for a disordered interacting system in one dimension using exact diagnonalization in the infinite temperature limit and provide strong evidence that single particle excitations carry signatures of delocalization to MBL transition. In the delocalized phase, the typical values of the local density of states and the scattering rate are finite while in the MBL phase, the typical values for both the quantities become vanishingly small. The probability distribution functions of the local density of states and the scattering rate are broad log-normal distributions in the delocalized phase while the distributions become very narrow and sharply peaked close to zero in the MBL phase. We also study the eigenstate Green's function for all the many-body eigenstates and demonstrate that both, the energy resolved typical scattering rate and the typical local density of states, can track the many-body mobility edges., Comment: A few changes to the text to improve clarity. No change in results. Close to the published version

The authors report on a mechanism of strong enhancement of the band Land\'e parameter $q$ due to in-plane confinement of holes and the valence-band warping. This explains the surprisingly large in-plane hole $g$ factor in symmetric self-assembled (In,Ga)As/GaAs quantum dots with $D2d$ symmetry as revealed by coherent optical spectroscopy. The proposed mechanism results in uniform magnetic field induced optical anisotropy for the entire quantum dot ensemble, which is a prerequisite for the realization of spin quantum memories and spin-photon entanglement in the ensemble.

Heavy fermion metals typically exhibit unconventional quantum critical point or quantum critical phase at zero temperature due to competition of Kondo effect and magnetism. Previous theories were often based on certain local type of assumptions and a fully consistent explanation of experiments has not been achieved. Here we develop an efficient algorithm for the Schwinger boson approach to explore the effect of spatial correlations on the Kondo lattice and introduce the concept of nonlocal Kondo effect in the quantum critical region with deconfined spinons. We predict a global phase diagram containing a non-Fermi liquid quantum critical phase with a hidden holon Fermi surface and a partially enlarged electron Fermi surface for strong quantum fluctuations while a single quantum critical point for weak quantum fluctuations. This explains the unusual metallic spin liquid recently reported in the frustrated Kondo lattice CePdAl and resolves the Fermi volume puzzle in YbRh$_2$Si$_2$. Our theory highlights the importance of nonlocal physics and provides a unified understanding of heavy fermion quantum criticality., 11 pages, 6 figures

We propose a mechanism to suppress heating in periodically driven many-body quantum systems by employing sufficiently long-range interactions and experimentally relevant initial conditions. The mechanism is robust to local perturbations and does \emph{not} rely on disorder or high driving frequencies. Instead, it makes use of an approximate fragmentation of the many-body spectrum of the non-driven system into bands, with band gaps that grow with the system size. We show that when these systems are driven, there is a regime where \emph{decreasing} the driving frequency \emph{decreases} heating and entanglement build-up. This is demonstrated numerically for a prototypical system of spins in one dimension, but the results can be readily generalized to higher dimensions., Comment: 5 pages, 4 figures

The interplay of disorder and strong correlations in quantum many-body systems remains an open question. That is despite much progress made in recent years with ultracold atoms in optical lattices to better understand phenomena such as many-body localization or the effect of disorder on Mott metal-insulator transitions. Here, we utilize the numerical linked-cluster expansion technique, extended to treat disordered quantum lattice models, and study exact thermodynamic properties of the disordered Fermi-Hubbard model on the square and cubic geometries. We consider box distributions for the disorder in the onsite energy, the interaction strength, as well as the hopping amplitude and explore how energy, double occupancy, entropy, heat capacity and magnetic correlations of the system in the thermodynamic limit evolve as the strength of disorder changes. We compare our findings with those obtained from determinant quantum Monte Carlo simulations and discuss the relevance of our results to experiments with cold fermionic atoms in optical lattices., 13 pages, 12 figures, same as the published version

At a discrete set of magic angles, twisted bilayer graphene has been shown to host extraordinarily flat bands, correlated insulating states, unconventional superconductivity, and distinct Landau level degeneracies. In this work, we design a highly efficient quantum Otto engine using a twisted bilayer graphene sample. Flat bands, which occur at magic angles, make the prospect of extracting useful work from our Otto engine lucrative. We use an eight-band continuum model of twisted bilayer graphene to compute efficiencies and work outputs for magic and non-magic angle twists, and compare the results with an $AB$ stacked bilayer and a monolayer. It is observed that the efficiency varies smoothly with the twist angle and the maximum is attained at the magic angle., Comment: 9 pages, 8 figures, accepted for publication in Physical Review B

The multipolar Kondo problem, wherein the quantum impurity carries higher-rank multipolar moments, has seen recent theoretical and experimental interest due to proposals of novel non-Fermi liquid states and the availability of a variety of material platforms. The multipolar nature of local moments, in conjunction with constraining crystal field symmetries, leads to a vast array of possible interactions and resulting non-Fermi liquid ground states. Previous works on Kondo physics have typically focussed on impurities that have two degenerate internal states. In this work, inspired by recent experiments on the tetragonal material YbRu$_{2}$Ge$_{2}$, which has been shown to exhibit a local moment with a quasi-fourfold degenerate ground state, we consider the Kondo effect for such a quasi-quartet multipolar impurity. In the tetragonal crystal field environment, the local moment supports dipolar, quadrupolar, and octupolar moments, which interact with conduction electrons in entangled spin and orbital states. Using renormalization group analysis, we uncover a number of emergent quantum ground states characterized by non-trivial fixed points. It is shown that these previously unidentified fixed points are described by truncated SU(4) Kondo models, where only some of the SU(4) generators (representing the impurity degrees of freedom) are coupled to conduction electrons. Such novel non-trivial fixed points are unique to the quasi-quartet multipolar impurity, reinforcing the idea that an unexplored rich diversity of phenomena may be produced by multipolar quantum impurity systems., Comment: 8+8 pages, 2 figures

We study the low frequency admittance of a quantum Hall bar of size much larger than the electronic coherence length. We find that this macroscopic conductor behaves as an ideal quantum conductor with vanishing longitudinal resistance and purely inductive behavior up to f, 4 pages article with 4 figures, submitted to Physical Review B Letters, concatenated with 12 pages supplementary information (having 15 figures) in a 17 pages article with concantenated bibliography

We use large-scale exact diagonalization to study the quantum Ising chain in a transverse field with long-range power-law interactions decaying with exponent $\alpha$. We numerically study various probes for quantum chaos and eigenstate thermalization {on} the level of eigenvalues and eigenstates. The level-spacing statistics yields a clear sign towards a Wigner-Dyson distribution and therefore towards quantum chaos across all values of $\alpha>0$. Yet, for $\alpha, Comment: 17 pages, 15 figures

The dynamical behavior of a quantum many-particle system is characterized by the lifetime of its excitations. When the system is perturbed, observables of any non-conserved quantity decay exponentially, but those of a conserved quantity relax to equilibrium with a power law. Such processes are associated with a dynamical exponent $z$ that relates the spread of correlations in space and time. We present numerical results for the Fredkin model, a quantum spin chain with a three-body interaction term, which exhibits an unusually large dynamical exponent. We discuss our efforts to produce a reliable estimate $z$=3.16(1) through direct simulation of the quantum evolution and to explain the slow dynamics in terms of an excited bond that executes a constrained random walk in Monte Carlo time., Comment: 11 pages, 9 figures

We investigate the fate of coherence in the dynamical evolution of a symmetry protected quantum system. Under the formalism of system-plus-bath for open quantum system, the anti-unitary symmetry exhibits significant difference from the unitary one in protecting initial coherence. Specifically, taking advantage of Lindblad master equation, we find that a pure state in the symmetry protected degenerate subspace will decohere even though both the system Hamiltonian and system-environment interaction respect the same anti-unitary symmetry. In contrast, the coherence will persist when the protecting symmetry is unitary. We provide an elaborate classification table to illustrate what kinds of symmetry combinations are able to preserve the coherence of initial state, which is confirmed by several concrete models in spin-$3/2$ system. Our results could help to explore the possible experimental realization of stable time-reversal symmetric topological states., Comment: 8 pages, 3 figures and 3 tables

Amorphous dielectric materials have been known to host two-level systems (TLSs) for more than four decades. Recent developments on superconducting resonators and qubits enable detailed studies on the physics of TLSs. In particular, measuring the loss of a device over long time periods (a few days) allows us to investigate stochastic fluctuations due to the interaction between TLSs. We measure the energy relaxation time of a frequency-tunable planar superconducting qubit over time and frequency. The experiments show a variety of stochastic patterns that we are able to explain by means of extensive simulations. The model used in our simulations assumes a qubit interacting with high-frequency TLSs, which, in turn, interact with thermally activated low-frequency TLSs. Our simulations match the experiments and suggest the density of low-frequency TLSs is about three orders of magnitude larger than that of high-frequency ones., Submitted for publication. 13 pages, 5 figures, and 3 tables. Code available at https://gitlab.com/DQMLab/qubitfluctuations

Interactions between particles in quantum many-body systems play a crucial role in determining the electric, magnetic, optical, and thermal properties of the system. The recent progress in the laser-pulse technique has enabled the manipulations and measurements of physical properties on ultrafast timescales. Here we propose a method for the direct and ultrafast probing of quantum many-body interaction through coherent two-dimensional (2D) spectroscopy. Using a two-band fermionic Hubbard model for the minimum two-site lattice system, we find that the 2D spectrum of a noninteracting system contains only diagonal peaks; the interparticle interaction manifests itself in the emergence of off-diagonal peaks in the 2D spectrum before all the peaks coalesce into a single diagonal peak as the system approaches the strongly interacting limit. The evolution of the 2D spectrum as a function of the time delay between the second and third laser pulses can provide important information on the ultrafast time variation of the interaction.

We study a model of $N$ fermions in a quantum dot, coupled to $M$ bosons by a disorder-induced complex Yukawa coupling [Yukawa Sachdev-Ye-Kitaev (SYK) model], in order to explore the interplay between non-Fermi liquid and superconductivity in a strongly coupled, (quantum-)critical environment. We analyze the phase diagram of the model for an arbitrary complex interaction and arbitrary ratio of $N/M$, with special focus on the two regimes of non-Fermi-liquid behavior: an SYK-like behavior with a power-law frequency dependence of the fermionic self-energy and an impuritylike behavior with frequency independent self-energy. We show that the crossover between the two can be reached by varying either the strength of the fermion-boson coupling or the ratio $M/N$. We next argue that in both regimes the system is unstable to superconductivity if the strength of time-reversal-symmetry-breaking disorder is below a certain threshold. We show how the corresponding onset temperatures vary between the two regimes. We argue that the superconducting state is highly unconventional with an infinite set of minima of the condensation energy at $T=0$, corresponding to topologically different gap functions. We discuss in detail similarities and differences between this model and the model of dispersion-full fermions tuned to a metallic quantum-critical point, with an effective singular dynamical interaction $V(\mathrm{\ensuremath{\Omega}})\ensuremath{\propto}1/{|\mathrm{\ensuremath{\Omega}}|}^{\ensuremath{\gamma}}$ (the $\ensuremath{\gamma}$ model).

Recent advances in quantum engineering have given us the ability to design hybrid systems with novel properties normally not present in the regime they operate in. The coupling of spin ensembles and magnons to microwave resonators has for instance lead to a much richer understanding of collective effects in these systems and their potential quantum applications. We can also hybridize electron and nuclear spin ensembles together in the solid-state regime to investigate collective effects normally only observed in the atomic, molecular and optical world. Here we explore in the solid state regime the dynamics of a double domain nuclear spin ensemble coupled to the Nambu-Goldstone boson in GaAs semiconductors and show it exhibits both collective and individual relaxation (thermalization) on very different time scales. Further the collective relaxation of the nuclear spin ensemble is what one would expect from superradiant decay. This opens up the possibility for the exploration of novel collective behaviour in solid state systems where the natural energies associated with those spins are much less than the thermal energy., Comment: 11 pages including supplementary material

Motivated by recent studies of symmetry protected topological states that are stabilized even in the absence of an energy gap, the authors study analytically the interaction of a (0+1)$D$ impurity spin, which in some cases may be viewed as a topological state bound to a lattice defect, with a (2+1)$D$ strongly interacting bulk, composed of bosonic excitations tuned to a quantum critical point. The question of whether the spin is (partially) screened is addressed within the framework of four different models, using mainly the large-$N$ technique. The authors also point out intriguing connections with the physics of the Sachdev-Ye-Kitaev model.

We study transport properties and the formation of bound states in the continuum (BIC) in asymmetric quantum mechanical and electromagnetic waveguides. An analytical model for an arbitrary asymmetric two-terminal quantum mechanical waveguide is proposed, and conditions of BIC formation are formulated. We show that the Friedrich-Wintgen mechanism of BIC formation in a system coupled to two continua takes place regardless of the symmetry of the system as long as the proportionate coupling condition is fulfilled. This result is illustrated by numerical simulation of two-dimensional quantum billiard and optical waveguide with a cavity. Due to the universal wave nature of BIC, the proposed BIC formation mechanism allows one to obtain BICs in the broader class of quantum mechanical, electromagnetic, acoustic, and other types of structures.

Understanding the spreading of the operator space entanglement entropy ($OSEE$) is key in order to explore out-of-equilibrium quantum many-body systems. Here we argue that for integrable models the dynamics of the $OSEE$ is related to the diffusion of the underlying quasiparticles. We derive the logarithmic bound $1/2\ln(t)$ for the $OSEE$ of some simple, i.e., low-rank, diagonal local operators. We numerically check that the bound is saturated in the rule $54$ chain, which is representative of interacting integrable systems. Remarkably, the same bound is saturated in the spin-1/2 Heisenberg $XXZ$ chain. Away from the isotropic point and from the free-fermion point, the $OSEE$ grows as $1/2\ln(t)$, irrespective of the chain anisotropy, suggesting universality. Finally, we discuss the effect of integrability breaking. We show that strong finite-time effects are present, which prevent from probing the asymptotic behavior of the $OSEE$., Comment: 9 pages, 10 figures. Expanded version. As accepted in PRB

The variational autoregressive network is extended to the Euclidean path integral representation of a quantum partition function. An essential challenge is adapting the sequential process of sample generation by an autoregressive network to a nonlocal constraint due to the periodic boundary condition in the path integral. An add-on oracle is devised for this purpose, which accurately identifies and stalls unviable configurations as soon as they occur. The oracle enables rejection-free sampling conforming to the periodic boundary condition. As a demonstration, the oracle-guided autoregressive network is applied to obtain variational solutions of quantum spin chains at finite temperatures with relatively large system sizes and numbers of time slicing, and to efficiently compute thermodynamic quantities.

The coherence-to-decoherence transition is studied in a nanowire modeled as a one-dimensional tight-binding lattice in the presence of an external field and in linear interaction with a boson heat bath, characterized by Ohmic dissipation. The focus of attention is the probability propagator which quantifies the likelihood of a quantum particle, such as an electron to end up at an arbitrary site at a time $t$, given that it was at the origin initially---and from it---the particle-current and the mean-squared displacement. If the bath is absent, the probability operator exhibits quantum coherence as can be captured by say, Bloch oscillation and Wannier-Stark (dynamic) localization. The coupling with the bath---which can be weak or strong---leads to decoherence that will be quantified in the text. The Ohmic model of the spectral function of bath excitations contains a cutoff frequency, which if greater than the temperature (in energy units) defines the ``low-temperature'' regime, whereas the opposite limit implies ``high temperatures.'' Results will be presented in both these regimes separately.

Studies of the current-induced spin polarization (CISP) have been recently reinvigorated due to the discoveries of CISP in some burgeoning materials such as oxide interfaces, van der Waals, and topological quantum materials. Here, we investigate the CISP in two-dimensional systems for different types of spin-orbit coupling (SOC) using the Boltzmann transport theory. We find an anisotropic response of CISP to the current direction which strongly depends on the type of SOC. We demonstrate that the CISP is nonlinear with respect to the SOC magnitude, depends on the Fermi energy, and exhibits two different transport regimes for low or high carrier density. Finally, we propose a magnetoresistance device which can exploit the predicted CISP anisotropy.