Test of quantum thermalization in the two-dimensional transverse-field Ising model

TL;DR

This study investigates whether a two-dimensional transverse-field Ising model thermalizes after quantum quenches, revealing that thermalization occurs only under certain conditions and depends on the quench parameters.

Contribution

The paper provides the first detailed analysis of thermalization in a non-integrable 2D quantum system using real-time variational Monte Carlo methods, highlighting parameter-dependent behavior.

Findings

Thermalization observed after paramagnetic phase quenches.

Deviations from thermal behavior in ferromagnetic phase quenches.

Memory of initial state persists even after strong quenches.

Abstract

We study the quantum relaxation of the two-dimensional transverse-field Ising model after global quenches with a real-time variational Monte Carlo method and address the question whether this non-integrable, two-dimensional system thermalizes or not. We consider both interaction quenches in the paramagnetic phase and field quenches in the ferromagnetic phase and compare the time-averaged probability distributions of non-conserved quantities like magnetization and correlation functions to the thermal distributions according to the canonical Gibbs ensemble obtained with quantum Monte Carlo simulations at temperatures defined by the excess energy in the system. We find that the occurrence of thermalization crucially depends on the quench parameters: While after the interaction quenches in the paramagnetic phase thermalization can be observed, our results for the field quenches in the ferromagnetic phase show clear deviations from the thermal system. These deviations increase with the quench strength and become especially clear comparing the shape of the thermal and the time-averaged distributions, the latter ones indicating that the system does not completely lose the memory of its initial state even for strong quenches. We discuss our results with respect to a recently formulated theorem on generalized thermalization in quantum systems.