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We study one-dimensional (1D) lattice anyons with extended Hubbard interactions at unit filling using bosonization and numerical simulations. The behavior can be continuously tuned from Bosonic to Fermionic behavior by adjusting the topological exchange angle $\theta$, which leads to a competition of different instabilities. We present the bosonization theory in presence of dynamic gauge fields, which predicts a phase diagrams of four different gapped phases with distinct dominant correlations. Advanced numerical simulations determine and analyze the exact phase transitions between Mott insulator, charge density wave, dimerized state, and Haldane insulator, all of which meet at a multi-critical line in the parameter space of anyonic angle $\theta$, onsite interaction $U$, and nearest neighbor repulsion $V$. Superfluid and pair-superfluid phases are stable in a region of small $V$., Comment: 16 pages, 9 figures, more details and the final version can be found at https://www.physik.uni-kl.de/eggert/

In ultracold atoms, achieving a period-$3$ structure poses a significant challenge. In this work, we propose a three-sublattice spin-flop transition mechanism, differing from the two-sublattice counterpart used to explain the emergence of ferrimagnetic orders in higher dimensions. Guided by this mechanism, we design a setup of alkaline-earth-metal atoms to create a spin-orbit coupled optical lattice, where we identify a triplet-fold degenerate $YX\bar{Y}$ state with a period-$3$ coplanar spin ordering within the deep Mott-insulating phase region of the ground-state phase diagram. The $YX\bar{Y}$ state is protected by a finite gap, and its characteristic angle can be finely tuned by specific setup parameters. Moreover, we use the Rabi spectroscopy technique to detect the $YX\bar{Y}$ state. Our work not only shows the feasibility of achieving a period-$3$ structure \textit{via} the new mechanism but also suggests its potential applications for exploring other periodic structures in optical lattices.

The application of the eigenstate thermalization hypothesis to non-Hermitian quantum systems has become one of the most important topics in dissipative quantum chaos, recently giving rise to intense debates. The process of thermalization is intricate, involving many time-evolution trajectories in the reduced Hilbert space of the system. By considering two different expansion forms of the density matrices adopted in the biorthogonal and right-state time evolutions, we have derived two versions of the Gorini-Kossakowski-Sudarshan-Lindblad master equations describing the non-Hermitian systems coupled to a bosonic heat bath in thermal equilibrium. By solving the equations, we have identified a sufficient condition for thermalization under both time evolutions, resulting in Boltzmann biorthogonal and right-eigenstate statistics, respectively. This finding implies that the recently proposed biorthogonal random matrix theory needs an appropriate revision. Moreover, we have exemplified the precise dynamics of thermalization and thermodynamic properties with test models., Comment: 5 pages, 4 figures (main text), 3 pages (supplementary material)

A biorthonormal-block density-matrix renormalization group algorithm is proposed to compute properties of non-Hermitian many-body systems, in which a renormalized-space partition to the non-Hermitian reduced density matrix is implemented to fulfill the prerequisite for the biorthonormality of the renormalization group (RG) transformation and to optimize the construction of saved Hilbert spaces. A redundancy in saved spaces of the reduced density matrix is exploited to reduce a condition number resulting from the non-unitarity of the left and right transformation matrices, in order to ensure the numerical stability of the RG procedure. The algorithm is successfully applied to an interacting fermionic Su-Schrieffer-Heeger model with nonreciprocal hoppings and staggered complex chemical potential, exhibiting novel many-body phenomena., Comment: 7+4 pages, 4+3 figures

The generation of nonuniform quadrupole states plays a crucial role in understanding various fascinating phenomena observed in the advancement of several research areas, e.g., multiferroic compounds, nonmagnetic superconductors, etc. In this work, we investigate the ground-state phase diagram of a generalized spin-3/2 bilinear-biquadratic-bicubic Heisenberg chain in the representation of multipolar operators. By numerical simulations with the large-scale density-matrix renormalization group (DMRG) method, we successfully identify a tetramerization phase and a stripe-Q phase. These phases are characterized by the emergence of nonuniform quadrupole orders resulting from the spontaneous breaking of translation symmetry. In particular, tetramerization phase refers to the quadrupole operators take a four-cycle, while the stripe-Q phase represents a striped pattern in quadrupole operators. Additionally, we demonstrate the presence of a Wess-Zumino-Witten (WZW) model with level k = 1 at the transition point between the dimerized (DM) phase and the Luttinger liquid (LL) phase, based on strong numerical findings.

The Haldane-Hubbard model is a prime example of the combined effects of band topology and electronic interaction. We revisit its spinful phase diagram at half-filling as a consensus on the presence of SU($2$) symmetry is currently lacking. To start, we utilize the Hartree-Fock mean-field method, which offers a direct understanding of symmetry breaking through the effective mass term that can acquire spin dependence. Our results, in agreement with previous studies, provide an instructive insight into the regime where the Chern number $C=1$, with only one spin species remaining topological. Besides that, we numerically study the phase diagram of the Haldane-Hubbard model via a large-scale infinite-density matrix renormalization group (iDMRG) method. The phase boundaries are determined by the Chern number and the correlation lengths obtained from the transfer-matrix spectrum. Unlike previous studies, the iDMRG method investigates the Haldane-Hubbard model on a thin and infinitely long cylinder and examines scenarios consistent with the two-dimensional thermodynamic limit. Here, the phase diagram we obtained qualitatively goes beyond the Hartree-Fock scope, particularly in the $C=1$ region, and serves as a quantitative benchmark for further theoretical and experimental investigations., Comment: 12 pages, 9 figures

The Kitaev-type spin chains have been demonstrated to be fertile playgrounds in which exotic phases and unconventional phase transitions are ready to appear. In this work, we use the density-matrix renormalization group method to study the quantum phase diagram of a spin-1 Kitaev chain with a tunable negative single-ion anisotropy (SIA). When the strength of the SIA is small, the ground state is revealed to be a spin-nematic phase which escapes conventional magnetic order but is characterized by a finite spin-nematic correlation because of the breaking spin-rotational symmetry. As the SIA increases, the spin-nematic phase is taken over by either a dimerized phase or an antiferromagnetic phase through an Ising-type phase transition, depending on the direction of the easy axis. For large enough SIA, the dimerized phase and the antiferromagnetic phase undergo a ``Landau-forbidden" continuous phase transition, suggesting new platform of deconfined quantum critical point in spin-1 Kitaev chain., Comment: 11+$\epsilon$ pages, 9 figures. Phys. Rev. B to appear

Charge stripes have been widely observed in many different types of unconventional superconductors, holding varying periods ($\mathcal{P}$) and intensities. However, a general understanding on the interplay between charge stripes and superconducting properties is still incomplete. Here, using large-scale unbiased numerical simulations on a general inhomogeneous Hubbard model, we discover that the charge-stripe period $\mathcal{P}$, which is variable in different real material systems, could dictate the pairing symmetries -- $d$ wave for $\mathcal{P} \ge 4$, $s$ and $d$ waves for $\mathcal{P} \le 3$. In the latter, tuning hole doping and charge-stripe amplitude can trigger a $d$-$s$ wave transition and magnetic-correlation shift, where the $d$-wave state converts to a pairing-density wave state, competing with the $s$ wave. These interesting phenomena arise from an unusual stripe-induced selection rule of pairing symmetries around on-stripe region and within inter-stripe region, giving rise to a critical point of $\mathcal{P}=3$ for the phase transition. In general, our findings offer new insights into the differences in the superconducting pairing mechanisms across many $\mathcal{P}$-dependent superconducting systems, highlighting the decisive role of charge stripe., Comment: 5 figures and 8 pages in main text, with a Supplemental Material which include 22 figures. Much more data by DQMC, DMRG and CPQMC are added. Awaiting resubmission

We investigate bipartite particle number fluctuations near the rank-$2$ exceptional points (EPs) of $\mathcal{PT}$-symmetric Su-Schrieffer-Heeger models. Beyond a conformal field theory of massless fermions, fluctuations or equivalently compressibility is negative definite and exhibits superinflation in leading order at EPs, due to the defectiveness in the biorthogonal Hilbert space. Associated with the bipartite von Neumann entanglement entropy, a parameter in an anomalous correspondence referencing from a purely non-Hermitian limit helps characterize two inequivalent EP sets. Our work paves the way for understanding the singularity of fluctuations relevant to EPs, more promisingly detectable in experiments., Comment: 13 pages, 3 + 5 figures

A neural network is a powerful tool that can uncover hidden laws beyond human intuition. However, it often appears as a black box due to its complicated nonlinear structures. By drawing upon the Gutzwiller mean-field theory, we can showcase a principle of sign rules for ordered states in qubit lattice models. We introduce a shallow feed-forward neural network with a single hidden neuron to present these sign rules. We conduct systematical benchmarks in various models, including the generalized Ising, spin-$1/2$ XY, (frustrated) Heisenberg rings, triangular XY antiferromagnet on a torus, and the Fermi-Hubbard ring at an arbitrary filling. These benchmarks show that all the leading-order sign rule characteristics can be visualized in classical forms, such as pitch angles. Besides, quantum fluctuations can result in an imperfect accuracy rate quantitatively., Comment: 12 pages, 11 figures

We propose an experimental realization of the time-periodically modulated Rabi frequency and suggest density-dependent hoppings of two species hardcore bosons in a one-dimensional optical lattice. Distinct from the previous work [Phys. Rev. Research {\bf 2}, 013275 (2020)], we study effects in the first resonance region. In the effective Hamiltonian, the intra-species hopping occurs only if the density discrepancy of the other species on these sites is zero, while the inter-species one is allowed once the relevant density discrepancy becomes nonzero. At integer-$1$ filling, the quantum phase diagram of the effective Hamiltonian is determined by the perturbation analysis together with numerical calculations. We find that in the limit of dominant $J_{1}$, the system becomes a double-degenerate dimerized state, with spontaneously breaking the translation symmetry. The interplay of $J_{0}$, $J_{1}$ and the fixed ${\bar U}=1$ leads to three BKT transition lines and a tricritical BKT point. Exact transition lines are obtained by the level spectroscopic technique. Besides, general physical properties, including the charge gap, neutral gap, superfluid density and dimerization strength, are investigated as well., Comment: 9 pages, 5 figures

We investigate the ground-state phase diagram of the spinless Haldane-Hubbard model in the presence of quenched disorder, contrasting results obtained from both exact diagonalization as well as density matrix renormalization group, applied to a honeycomb cylinder. The interplay of disorder, interactions and topology gives rise to a rich phase diagram, and in particular highlights the possibility of a disorder-driven trivial-to-topological transition in the presence of finite interactions. That is, the topological Anderson insulator, demonstrated in non-interacting settings, is shown to be stable to the presence of sufficiently small interactions before a charge density wave Mott insulator sets in. We further perform a finite-size analysis of the transition to the ordered state in the presence of disorder, finding a mixed character of first and second order transitions in finite lattices, tied to specific conditions of disorder realizations and boundary conditions used., Comment: 10 pages, 10 figures; as published

One-dimensional gapped phases that avoid any symmetry breaking have drawn enduring attention. In this paper, we study such phases in a bond-alternating spin-1 $K$-$\Gamma$ chain built of a Kitaev ($K$) interaction and an off-diagonal $\Gamma$ term. In the case of isotropic bond strength, a Haldane phase, which resembles the ground state of a spin-$1$ Heisenberg chain, is identified in a wide region. A gapped Kitaev phase situated at dominant ferromagnetic and antiferromagnetic Kitaev limits is also found. The Kitaev phase has extremely short-range spin correlations and is characterized by finite $\mathbb{Z}_2$-valued quantities on bonds. Its lowest entanglement spectrum is unique, in contrast to the Haldane phase whose entanglement spectrum is doubly degenerate. In addition, the Kitaev phase shows a double-peak structure in the specific heat at two different temperatures. In the pure Kitaev limit, the two peaks are representative of the development of short-range spin correlation at $T_h \simeq 0.5680$ and the freezing of $\mathbb{Z}_2$ quantities at $T_l \simeq 0.0562$, respectively. By considering bond anisotropy, regions of Haldane phase and Kitaev phase are enlarged, accompanied by the emergence of dimerized phases and three distinct magnetically ordered states., Comment: 14 pages, 13 figures. For a previous spin-1/2 analogy, see arXiv:2012.03382

We investigate the ground-state phase diagram of the spinful extended Haldane-Hubbard model on the honeycomb lattice using an exact-diagonalization, mean-field variational approach, and further complement it with the infinite density matrix renormalization group, applied to an infinite honeycomb cylinder. This model, governed by both on-site and nearest-neighbor interactions, can result in two types of insulators with finite local order parameters, either with spin or charge ordering. Moreover, a third one, a topologically nontrivial insulator with nonlocal order, is also manifest. We test expectations of previous analyses in spinless versions asserting that once a local order parameter is formed, the topological characteristics of the ground state, associated with a finite Chern number, are no longer present, resulting in a topologically trivial wave function. Our study confirms this overall picture, and highlights how finite-size effects may result in misleading conclusions on the coexistence of finite local order parameters and nontrivial topology in this model., Comment: 11 pages, 8 figures

We study the spin liquid candidate of the spin-$1/2$ $J_1$-$J_2$ Heisenberg antiferromagnet on the triangular lattice by means of density matrix renormalization group (DMRG) simulations. By applying an external Aharonov-Bohm flux insertion in an infinitely long cylinder, we find unambiguous evidence for gapless $U(1)$ Dirac spin liquid behavior. The flux insertion overcomes the finite size restriction for energy gaps and clearly shows gapless behavior at the expected wave-vectors. Using the DMRG transfer matrix, the low-lying excitation spectrum can be extracted, which shows characteristic Dirac cone structures of both spinon-bilinear and monopole excitations. Finally, we confirm that the entanglement entropy follows the predicted universal response under the flux insertion., Comment: 4+8 pages, 4+13 figures

We consider two species of hard-core bosons with density dependent hopping in a one-dimensional optical lattice, for which we propose experimental realizations using time-periodic driving. The quantum phase diagram for half-integer filling is determined by combining different advanced numerical simulations with analytic calculations. We find that a reduction of the density-dependent hopping induces a Mott-insulator to superfluid transition. For negative hopping a previously unknown state is found, where one species induces a gauge phase of the other species, which leads to a superfluid phase of gauge-paired particles. The corresponding experimental signatures are discussed., Comment: 20 pages, 9 figures, more information and final version can be found at this link: https://www.physik.uni-kl.de/eggert/papers/index.html

We investigate a spin-$1/2$ two-leg honeycomb ladder with frustrating next-nearest-neighbor (NNN) coupling along the legs, which is equivalent to two $J_1$-$J_2$ spin chains coupled with $J_\perp$ at odd rungs. The full parameter region of the model is systematically studied using conventional and infinite density-matrix renormalization group as well as bosonization. The rich phase diagram consists of five distinct phases: A Haldane phase, a NNN-Haldane phase and a staggered dimer phase when $J_{\perp} < 0$; a rung singlet phase and a columnar dimer phase when $J_{\perp} > 0$. An interesting reentrant behavior from the dimerized phase into the Haldane phase is found as the frustration $J_2$ increases. The universalities of the critical phase transitions are fully analyzed. Phase transitions between dimerized and disordered phases belong to the two-dimensional Ising class with central charge $c=1/2$. The transition from the Haldane phase to NNN-Haldane phase is of a weak topological first order, while the continuous transition between the Haldane phase and rung singlet phase has central charge $c=2$., Comment: 14 pages, 17 figures, for latest version and additional information see https://www.physik.uni-kl.de/eggert/papers/index.html

Motivated by the recent experiment on a rare-earth material YbMgGaO$_4$ [Y. Li \textit{et al.}, Phys. Rev. Lett. \textbf{115}, 167203 (2015)], which found that the ground state of YbMgGaO$_4$ is a quantum spin liquid, we study the ground-state phase diagram of an anisotropic spin-$1/2$ model that was proposed to describe YbMgGaO$_4$. Using the density-matrix renormalization group method in combination with the exact diagonalization, we calculate a variety of physical quantities, including the ground-state energy, the fidelity, the entanglement entropy and spin-spin correlation functions. Our studies show that in the quantum phase diagram there is a $120^{\circ}$ phase and two distinct stripe phases. The transitions from the two stripe phases to the $120^{\circ}$ phase are of the first order. However, the transition between the two stripe phases is not the first order, which is different from its classical counterpart. Additionally, we find no evidence for a quantum spin liquid in this model. Our results suggest that additional terms may be also important to model the material YbMgGaO$_4$. These findings will stimulate further experimental and theoretical works in understanding the quantum spin liquid ground state in YbMgGaO$_4$., Comment: minor changes

We study the thermodynamics of an XYZ Heisenberg chain with Dzyaloshinskii-Moriya interaction, which describes the low-energy behaviors of a one-dimensional spin-orbit-coupled bosonic model in the deep insulating region. The entropy and the specific heat are calculated numerically by the quasi-exact transfer-matrix renormalization group. In particular, in the limit $U^\prime/U\rightarrow\infty$, our model is exactly solvable and thus serves as a benchmark for our numerical method. From our data, we find that for $U^\prime/U>1$ a quantum phase transition between an (anti)ferromagnetic phase and a Tomonaga-Luttinger liquid phase occurs at a finite $\theta$, while for $U^\prime/U<1$ a transition between a ferromagnetic phase and a paramagnetic phase happens at $\theta=0$. A refined ground-state phase diagram is then deduced from their low-temperature behaviors. Our findings provide an alternative way to detect those distinguishable phases experimentally., Comment: accepted by Phys. Rev. B, title changed

We investigate the extended hard-core Bose-Hubbard model on the triangular lattice as a function of spatial anisotropy with respect to both tunneling and nearest-neighbor interaction strength. At half-filling the system can be tuned from decoupled one-dimensional chains to a two-dimensional solid phase with alternating density order by adjusting the anisotropic coupling. At intermediate anisotropy, however, frustration effects dominate and an incommensurate supersolid phase emerges, which is characterized by incommensurate density order as well as an anisotropic superfluid density. We demonstrate that this intermediate phase results from the proliferation of topological defects in the form of quantum bosonic domain walls. Accordingly, the structure factor has peaks at wave vectors, which are linearly related to the number of domain walls in a finite system in agreement with extensive quantum Monte Carlo simulations. We discuss possible connections with the supersolid behavior in the high-temperature superconducting striped phase., Comment: 8 pages, 8 figures. Latest version and more information at http://www.physik.uni-kl.de/eggert/papers/index.html

By performing large-scale density-matrix renormalization group simulations, we investigate a one-dimensional correlated bosonic lattice model with a synthetic spin-orbit coupling realized in recent experiments. In the insulating regime, this model exhibits a symmetry-protected topological phase. This symmetry-protected topological phase is stabilized by time-reversal symmetry and it is identified as a Haldane phase. We confirm our conclusions further by analyzing the entanglement spectrum. In addition, we find four conventional phases: a Mott insulating phase with no long range order, a ferromagnetic superfluid phase, a ferromagnetic insulating phase and a density-wave phase., Comment: Submitted on April 12, 2015, accepted by PRL

We study the evolution of magnetic structure driven by a synthetic spin-orbit coupling in a one-dimensional two-component Bose-Hubbard model. In addition to the Mott insulator-superfluid transition, we found in Mott insulator phases a transition from a gapped ferromagnetic phase to a gapless chiral phase by increasing the strength of spin-orbit coupling. Further increasing the spin-orbit coupling drives a transition from the gapless chiral phase to a gapped antiferromagnetic phase. These magnetic structures persist in superfluid phases. In particular, in the chiral Mott insulator and chiral superfluid phases, incommensurability is observed in characteristic correlation functions. These unconventional Mott insulator phase and superfluid phase demonstrate the novel effects arising from the competition between the kinetic energy and the spin-orbit coupling., Comment: 9 fig; English polished, note added

We investigate the effect of the Berry phase on quadrupoles that occur for example in the low-energy description of spin models. Specifically we study here the one-dimensional bilinear-biquadratic spin-one model. An open question for many years about this model is whether it has a non-dimerized fluctuating nematic phase. The dimerization has recently been proposed to be related to Berry phases of the quantum fluctuations. We use an effective low-energy description to calculate the scaling of the dimerization according to this theory, and then verify the predictions using large scale density-matrix renormalization group (DMRG) simulations, giving good evidence that the state is dimerized all the way up to its transition into the ferromagnetic phase. We furthermore discuss the multiplet structure found in the entanglement spectrum of the ground state wave functions., Comment: 4.5 pages + 4 pages supplementary material, 4 figures

We study the effect of the synthetic spin-orbit coupling in a two-component Bose-Hubbard model in one dimension by employing the density-matrix renormalization group method. A ferromagnetic long-range order emerges in both Mott insulator and superfluid phases resulting from the spontaneous breaking of the $Z_2$ symmetry, when the spin-orbit coupling term becomes comparable to the hopping kinetic energy and the inter-component interaction is smaller than the intra-one as well. This novel effect is expected to be detectable with the present realization of the synthetic spin-orbit coupling in experiments., Comment: 7 pages, 8 figures

We present exact results for the electronic transport properties of graphene sheets connected to two metallic electrodes. Our results, obtained by transfer-matrix methods, are valid for all sheet widths and lengths. In the limit of large width-to-length ratio relevant to recent experiments, we find a Dirac-point conductivity of $2e^2/\sqrt{3}h$ and a sub-Poissonian Fano factor of $2 - 3\sqrt{3}/\pi \simeq 0.346$ for armchair graphene; for the zigzag geometry these are respectively 0 and 1. Our results reflect essential effects from both the topology of graphene and the electronic structure of the leads, giving a complete microscopic understanding of the unique intrinsic transport in graphene., Comment: 4 pages,4figures