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

TL;DR

This study confirms that the two-dimensional XXZ model exhibits eigenstate thermalization, with numerical evidence supporting ETH validity across different symmetries and subspaces, up to moderate system sizes.

Contribution

It provides the first detailed numerical analysis of ETH in the 2D XXZ model, including cases with and without SU(2) symmetry, using exact diagonalization techniques.

Findings

ETH holds in the 2D XXZ model for various system sizes.

Eigenstate thermalization is valid within each total spin subspace.

The model's symmetry properties influence the ETH behavior.

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.