Eigenstate thermalization in the two-dimensional transverse field Ising model

TL;DR

This paper investigates how eigenstate thermalization manifests in the 2D transverse field Ising model, showing that quantum chaos and thermalization occur under certain conditions using exact diagonalization.

Contribution

It provides a detailed finite size scaling analysis demonstrating eigenstate thermalization in the 2D-TFIM with non-zero fields, expanding understanding of thermalization in quantum many-body systems.

Findings

Quantum chaos indicators suggest thermalization occurs with non-zero fields.

Eigenstate thermalization is observed in both ferromagnetic and antiferromagnetic cases.

Finite size scaling confirms the onset of thermalization under specific conditions.

Abstract

We study the onset of eigenstate thermalization in the two-dimensional transverse field Ising model (2D-TFIM) in the square lattice. We consider two non-equivalent Hamiltonians: the ferromagnetic 2D-TFIM and the antiferromagnetic 2D-TFIM in the presence of a uniform longitudinal field. We use full exact diagonalization to examine the behavior of quantum chaos indicators and of the diagonal matrix elements of operators of interest in the eigenstates of the Hamiltonian. A finite size scaling analysis reveals that quantum chaos and eigenstate thermalization occur in those systems whenever the fields are nonvanishing and not too large.