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

Jae Dong Noh

Published 2022-10-26Version 1

We investigate the eigenstate thermalization properties of the spin-1/2 XXZ model in the two-dimensional rectangular lattices of size $L_1\times L_2$ under the periodic boundary conditions. Exploiting the symmetry property, we can perform the 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 the 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.