XXZ Model Research Articles

Exact solution of long-range stabilizer Rényi entropy in the dual-unitary XXZ model*

Exact solution of long-range stabilizer Rényi entropy in the dual-unitary XXZ model*

Nonequilibrium Steady States in the Weakly-Coupled XXZ Model

Nonequilibrium Steady States in the Weakly-Coupled XXZ Model

Surface energy and elementary excitations of the XYZ spin chain with integrable open boundary fields

We study the thermodynamic limit of the anisotropic XYZ spin chain with non-diagonal integrable open boundary conditions. Although the U(1)-symmetry is broken, by using the new parametrization scheme, we exactly obtain the surface energy and the excitation energy of the system, which has solved the difficulty in the inhomogeneous T − Q relation. With the boundary parameters in the regions making the Hamiltonian Hermitian, we have obtained the distribution patterns of the zeros of the eigenvalue of the transfer matrix for the ground state and the excited ones. We find that the surface and excitation energies depend on the parities of sites number N, due to the long-range Neel order in the bulk. The easy-axis and thermodynamic limit for all the regions of boundary parameters are studied. We also obtain the physical quantities in the thermodynamic limit of boundary XXZ model by taking the trigonometric limit.

Emergent Berezinskii-Kosterlitz-Thouless and Kugel-Khomskii Physics in the Triangular Lattice Bilayer Colbaltate.

Motivated by the experiments on the triangular lattice bilayer colbaltate K_{2}Co_{2}(SeO_{3})_{3}, we consider an extended XXZ model to explore the underlying physics. The model is composed of interacting Co^{2+} dimers on the triangular lattice, where the Co^{2+} ion provides an effective spin-1/2 local moment via the spin-orbit coupling and the crystal field effect. The intradimer interaction is dominant and would simply favor the local spin singlet, and the interdimer interactions compete with the interdimer interaction, leading to rich behaviors. With the easy-axis anisotropy, it is shown that, in the ground state manifold of the intradimer Ising interaction, the system realizes an effective quantum Ising model, where the ground state is either a three-sublattice order with a mixture of antiferromagnetic Ising order and a valence-bond spin singlet or Ising disordered. The finite temperature regime realizes the Berezinskii-Kosterlitz-Thouless physics. To explore the full excitations, we incorporate the excited state manifold of the intradimer Ising interaction and establish the emergent Kugel-Khomskii physics. Thus, the triangular lattice bilayer colbaltate is an excellent platform to explore the interplay between geometrical frustration and anisotropic interactions as well as the emergent effective models and the resulting physics.

Worldsheet kinematics, dressing factors and odd crossing in mixed-flux AdS3 backgrounds

String theory on AdS3 × S3 × T4 geometries supported by a combination of NS-NS and R-R charges is believed to be integrable. We elucidate the kinematics and analytic structure of worldsheet excitations in mixed charge and pure NS-NS backgrounds, when expressed in momentum, Zhukovsky variables and the rapidity u which appears in the quantum spectral curve. We discuss the relations between fundamental and bound state excitations and the role of fusion in constraining and determining the S matrices of these theories. We propose a scalar dressing factor consistent with a novel u-plane periodicity and comment on its close relation to the XXZ model at roots of unity. We solve the odd part of crossing and show that our solution is consistent with fusion and reduces in the relativistic limit to dressing phases previously found in the literature.

Interaction-Driven Instabilities in the Random-Field XXZ Chain.

Despite enormous efforts devoted to the study of the many-body localization (MBL) phenomenon, the nature of the high-energy behavior of the Heisenberg spin chain in a strong random magnetic field is lacking consensus. Here, we take a step back by exploring the weak interaction limit starting from the Anderson localized (AL) insulator. Through shift-invert diagonalization, we find that, below a certain disorder threshold h^{*}, weak interactions necessarily lead to an ergodic instability, whereas at strong disorder the AL insulator directly turns into MBL, in agreement with a simple interpretation of the avalanche theory for restoration of ergodicity. We further map the phase diagram for the generic XXZ model in the disorder h-interaction Δ plane. Taking advantage of the total magnetization conservation, our results unveil the remarkable behavior of the spin-spin correlation functions: in the regime indicated as MBL by standard observables, their exponential decay undergoes an inversion of orientation ξ_{z}>ξ_{x}. We find that the longitudinal length ξ_{z} is a key quantity for capturing ergodic instabilities, as it increases with system size near the thermal phase, in sharp contrast to its transverse counterpart.

Non-Hermitian linear-response theory for spin diffusion in quantum systems

Spin transport theory of non-Hermitian quantum systems, where the non-Hermiticity led to a series of exotic phenomena when the system experiences dissipation to an environment is proposed. The goal is a better understanding of the spin diffusion in the one-dimensional non-Hermitian XXZ model which allows the transport coefficients be computed analytically. Moreover, we analyzed the electric transport in the one-dimensional non-Hermitian Hubbard model which is a very important model of electrons strongly correlated, where we have investigated the effect of non-Hermitian parameters like the imaginary hopping on AC and DC conductivities of the system. We analyzed the large U limit of this model, where such non-Hermiticity contributes with a minus sign in the virtual exchange of quasiparticles and the behavior of the ground state energy and low-lying excitations is reversed.

Entropic uncertainty relations and quantum coherence in the two-dimensional XXZ spin model with Dzyaloshinskii–Moriya interaction

Quantum renormalization group (QRG) is a tractable method for studying the criticalities of one-dimensional (1D) and two-dimensional (2D) many-body systems. By employing the QRG method, we first derive the effective Hamiltonian and QRG equations of a 2D XXZ model with Dzyaloshinskii–Moriya (DM) interaction analytically. The linear-entropy-based uncertainty, the quantum discord (QD), and the multipartite quantum coherence based on the square root of the quantum Jensen–Shannon divergence of the 2D XXZ model are then studied as the indicators of quantum phase transitions (QPTs). The nonanalytic and scaling behaviors of the uncertainty, QD and quantum coherence are also analyzed through numerical calculations. Moreover, we investigate the effect of the easy-axis anisotropy parameter and DM interaction on the QPT. We find that the uncertainty, QD, and quantum coherence can all be utilized to detect QPTs. Our findings could shed new light on the observable of the QPT of the many-body system with the uncertainty and quantum coherence, and enrich the application of QRG method to Heisenberg spin models.

Learning quantum phases via single-qubit disentanglement

Identifying phases of matter presents considerable challenges, particularly within the domain of quantum theory, where the complexity of ground states appears to increase exponentially with system size. Quantum many-body systems exhibit an array of complex entanglement structures spanning distinct phases. Although extensive research has explored the relationship between quantum phase transitions and quantum entanglement, establishing a direct, pragmatic connection between them remains a critical challenge. In this work, we present a novel and efficient quantum phase transition classifier, utilizing disentanglement with reinforcement learning-optimized variational quantum circuits. We demonstrate the effectiveness of this method on quantum phase transitions in the transverse field Ising model (TFIM) and the XXZ model. Moreover, we observe the algorithm's ability to learn the Kramers-Wannier duality pertaining to entanglement structures in the TFIM. Our approach not only identifies phase transitions based on the performance of the disentangling circuits but also exhibits impressive scalability, facilitating its application in larger and more complex quantum systems. This study sheds light on the characterization of quantum phases through the entanglement structures inherent in quantum many-body systems.

Study of the Berezinskii–Kosterlitz–Thouless transition: an unsupervised machine learning approach

The Berezinskii–Kosterlitz–Thouless (BKT) transition in magnetic systems is an intriguing phenomenon, and estimating the BKT transition temperature is a long-standing problem. In this work, we explore anisotropic classical Heisenberg XY and XXZ models with ferromagnetic exchange on a square lattice and antiferromagnetic exchange on a triangular lattice using an unsupervised machine learning approach called principal component analysis (PCA). The earlier PCA studies of the BKT transition temperature ( TBKT ) using the vorticities as input fail to give any conclusive results, whereas, in this work, we show that the proper analysis of the first principal component-temperature curve can estimate TBKT which is consistent with the existing literature. This analysis works well for the anisotropic classical Heisenberg with a ferromagnetic exchange on a square lattice and for frustrated antiferromagnetic exchange on a triangular lattice. The classical anisotropic Heisenberg antiferromagnetic model on the triangular lattice has two close transitions: the TBKT and Ising-like phase transition for chirality at Tc , and it is difficult to separate these transition points. It is also noted that using the PCA method and manipulation of their first principal component not only makes the separation of transition points possible but also determines transition temperature.

Emergent anomalous hydrodynamics at infinite temperature in a long-range XXZ model

Emergent anomalous hydrodynamics at infinite temperature in a long-range XXZ model

Quantum correlation, entanglement in the kagome lattice non-Hermitian quantum systems

Quantum correlation in the antiferromagnetic XXZ model on kagome lattice and non-Hermitian tight binding model on kagome lattice are investigated. For the Hermitian XXZ model on kagome lattice, the calculations are performed for different extensions of the model with single-ion anisotropy and out-of-plane Dzyaloshinskii–Moriya interaction (DMI). We get the von Neumann entropy as a function of the DMI interaction, anisotropy and single-ion anisotropy with aim to verify the effect of these corrections that occurs in real magnetic systems on quantum correlation. Moreover, the effect of DMI interaction, anisotropy and single-ion anisotropy is investigated on concurrence and entanglement negativity as well. For the non-Hermitian tight binding model on kagome lattice, we analyzed quantum correlation using the entanglement negativity as entanglement measure which is more adequate in this case.

Continuous-time worm quantum Monte Carlo study of a two-dimensional spin-one XXZ model

Continuous-time worm quantum Monte Carlo study of a two-dimensional spin-one XXZ model

Dynamics of Quantum Correlation in a Two‐qutrit Heisenberg XXZ Model with Heitler‐London and Dzyaloshinskii‐Moriya Couplings

AbstractThis study investigates the dynamics of quantum coherence and entanglement in the spin‐1 Heisenberg XXZ model. Particularly, the effects of the Heitler‐London (HL) coupling and the Dzyaloshinskii‐Moriya (DM) interaction are examined. By utilizing tools from quantum information theory, the concept of quantum correlated coherence and negativity are explored. The results show intrinsic decoherence leads to a decay of both correlated coherence and negativity. Interestingly, it is found that a small value of the Dzyaloshinskii‐Moriya interaction can significantly enhance coherence and entanglement. Various factors influence the system dynamics, including the initial state, anisotropy parameter, and the coupling distance between spins. It is shown that, by fixing the anisotropy parameter, the isotropic Heisenberg models XX and XXX can be easily recovered. Ultimately, the findings highlight that the system maintains a coherent temporal evolution despite decoherence.

Programmable order by disorder effect and underlying phases through dipolar quantum simulators

In this work, we study two different quantum simulators composed of molecules with dipole-dipole interaction through various theoretical and numerical tools. Our first result provides knowledge of the quantum order by disorder effect of the S=1/2 system, which is programmable in a quantum simulator composed of circular Rydberg atoms in the triangular optical lattice with a controllable diagonal anisotropy. When the numbers of up spins and down spins are equal, a set of subextensive degenerate ground states is present in the classical limit, composed of continuous strings whose configuration enjoys a large degree of freedom. Among all possible configurations, we focus on the stripe (up and down spins aligning straightly) and kinked (up and down spins forming zigzag spin chains) patterns. Adopting the the real space perturbation theory, we estimate the leading order energy correction when the nearest-neighbor spin exchange coupling, J, is considered, and the overall model becomes an effective XXZ model with a spatial anisotropy. Our calculation demonstrates a lifting of the degeneracy, favoring the stripe configuration. When J becomes larger, we adopt the infinite projected entangled-pair state (iPEPS) and numerically check the effect of degeneracy lifting. The iPEPS results show that even when the spin exchange coupling is strong the stripe pattern is still favored. Next, we study the dipolar bosonic model with tilted polar angle which can be realized through a quantum simulator composed of cold atomic gas with dipole-dipole interaction in an optical lattice. By placing the atoms in a triangular lattice and tilting the polar angle, the diagonal anisotropy can also be realized in the bosonic system. With our cluster mean-field theory calculation, we provide various phase diagrams with different tilted angles, showing the abundant underlying phases including the supersolid. Our proposal indicates realizable scenarios through quantum simulators in studying the quantum effect as well as extraordinary phases. We believe that our results indicated here can also become a good benchmark for two-dimensional quantum simulators. Published by the American Physical Society 2024

Quantized Berry Phase in the Spin-1/2 XXZ Model on the Anisotropic Kagome Lattice

Quantized Berry Phase in the Spin-1/2 XXZ Model on the Anisotropic Kagome Lattice

Frustration—no frustration crossover and phase transitions in 2D spin models with zig-zag structures

Three 2D spin models made of frustrated zig-zag chains with competing interactions which, by exact summation with respect to some degrees of freedom, can be replaced by an effective temperature-dependent interaction, were considered. The first model, exactly solvable Ising chains coupled by only four-spin interactions, does not exhibit any finite temperature phase transition; nevertheless, temperature can trigger a frustration–no frustration crossover accompanied by gigantic specific heat. A similar effect was observed in several two-leg ladder models (Weiguo 2020 arXiv:2006.08921v2; 2020 2006.15087v1). The anisotropic Ising chains coupled by a direct interchain interaction and, competing with it, indirect interaction via spins located between chains, are analyzed using the exact Onsager’s equation and linear perturbation renormalization group (LPRG). Depending on the parameter set, such a model exhibits one antiferromagnetic (AF) or ferromagnetic (FM) phase transition or three phase transitions with a re-entrant disordered phase between AF and FM ones. The LPRG method was also used to study coupled uniaxial XXZ chains which, for example, can be a minimal model to describe the magnetic properties of compounds in which uranium and rare earth atoms form zig-zag chains. As with the Ising model, for a certain set of parameters, the model can undergo three phase transitions. However, both intrachain and interchain plain interactions si,jxsk,lx+si,jysk,ly can eliminate the re-entrant disordered phase, and then only one transition takes place. Additionally, the XXZ model can undergo temperature-induced metamagnetic transition.

The generalization of strong anisotropic XXZ model and UC hierarchy

The generalization of strong anisotropic XXZ model and UC hierarchy

Entanglement entropy of two disjoint intervals and spin structures in interacting chains in and out of equilibrium

We take the paradigm of interacting spin chains, the Heisenberg spin-12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{2} $$\\end{document} XXZ model, as a reference system and consider interacting models that are related to it by Jordan-Wigner transformations and restrictions to sub-chains. An example is the fermionic analogue of the gapless XXZ Hamiltonian, which, in a continuum scaling limit, is described by the massless Thirring model. We work out the Rényi-α entropies of disjoint blocks in the ground state and extract the universal scaling functions describing the Rényi-α tripartite information in the limit of infinite lengths. We consider also the von Neumann entropy, but only in the limit of large distance. We show how to use the entropies of spin blocks to unveil the spin structures of the underlying massless Thirring model. Finally, we speculate about the tripartite information after global quenches and conjecture its asymptotic behaviour in the limit of infinite time and small quench. The resulting conjecture for the “residual tripartite information”, which corresponds to the limit in which the intervals’ lengths are infinitely larger than their (large) distance, supports the claim of universality recently made studying noninteracting spin chains. Our mild assumptions imply that the residual tripartite information after a small quench of the anisotropy in the gapless phase of XXZ is equal to − log 2.

Dualities in One-Dimensional Quantum Lattice Models: Topological Sectors

It has been a long-standing open problem to construct a general framework for relating the spectra of dual theories to each other. Here, we solve this problem for the case of one-dimensional quantum lattice models with symmetry-twisted boundary conditions. In Ref. [PRX Quantum 4, 020357], dualities are defined between (categorically) symmetric models that only differ in a choice of module category. Using matrix product operators, we construct from the data of module functors explicit symmetry operators preserving boundary conditions as well as intertwiners mapping topological sectors of dual models onto one another. We illustrate our construction with a family of examples that are in the duality class of the spin-12 Heisenberg XXZ model. One model has symmetry operators forming the fusion category Rep(S3) of representations of the group S3. We find that the mapping between its topological sectors and those of the XXZ model is associated with the nontrivial braided autoequivalence of the Drinfel’d center of Rep(S3). Published by the American Physical Society 2024