Eigenstate thermalization hypothesis in two-dimensional XXZ model with or without SU(2) symmetry

Abstract

We investigate the eigenstate thermalization properties of the spin-1/2 $XXZ$ model in two-dimensional rectangular lattices of size $L_1\times L_2$ under periodic boundary conditions. Exploiting the symmetry property, we can perform an exact diagonalization study of the energy eigenvalues up to system size $4\times 7$ and of the energy eigenstates up to $4\times 6$. Numerical analysis of the Hamiltonian eigenvalue spectrum and matrix elements of an observable in the Hamiltonian eigenstate basis supports that the two-dimensional $XXZ$ model follows the eigenstate thermalization hypothesis. When the spin interaction is isotropic the $XXZ$ model Hamiltonian conserves the total spin and has SU(2) symmetry. We show that the eigenstate thermalization hypothesis is still valid within each subspace where the total spin is a good quantum number.

final version. 9 pages with 10 figures

References in corpus (18)

• Thermalization and its mechanism for generic isolated quantum systems
• Localization of interacting fermions at high temperature
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Experimental Observation of a Generalized Gibbs Ensemble
• Breakdown of thermalization in finite one-dimensional systems
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• Generalized Thermalization in an Integrable Lattice System
• Dynamical Correlations after a Quantum Quench
• Eigenstate thermalization within isolated spin-chain systems
• Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
• Eigenstate thermalization and quantum chaos in the Holstein polaron model
• Calculating the energy spectra of magnetic molecules: application of real- and spin-space symmetries
• Operator growth in the transverse-field Ising spin chain with integrability-breaking longitudinal field
• Non-Abelian symmetry can increase entanglement entropy
• Eigenstate thermalization hypothesis in quantum dimer models
• Optimized implementation of the Lanczos method for magnetic systems
• Combined use of translational and spin-rotational invariance for spin systems
• Guide to Exact Diagonalization Study of Quantum Thermalization

Cited by in corpus (10)

• Noncommuting conserved charges in quantum thermodynamics and beyond
• Non-Abelian transport distinguishes three usually equivalent notions of entropy production
• Average pure-state entanglement entropy in spin systems with SU(2) symmetry
• Violation of Eigenstate Thermalization Hypothesis in Quantum Field Theories with Higher-Form Symmetry
• Non-abelian symmetry-resolved entanglement entropy
• Noncommuting charges can remove non-stationary quantum many-body dynamics
• Eigenstate thermalization in spin-$\frac{1}{2}$ systems with SU(2) symmetry
• Remarks on effects of projective phase on eigenstate thermalization hypothesis
• Proof of absence of local conserved quantities in two- and higher-dimensional quantum Ising models
• Numerical evidence for the non-Abelian eigenstate thermalization hypothesis