Quench Dynamics in Randomly Generated Extended Quantum Models

TL;DR

This paper investigates how quantum systems with randomly generated Hamiltonians thermalize after a quench, focusing on the Eigenstate Thermalization Hypothesis and differences between dense and sparse matrix models.

Contribution

It provides a comparative analysis of dense and sparse random matrix models in quantum thermalization, highlighting the role of rare states and finite size effects.

Findings

Sparse matrices show different observable distributions compared to dense matrices.

Evidence supports the existence of rare states with atypical observable values.

Finite size scaling of thermalization time scales is characterized.

Abstract

We analyze the thermalization properties and the validity of the Eigenstate Thermalization Hypothesis in a generic class of quantum Hamiltonians where the quench parameter explicitly breaks a Z_2 symmetry. Natural realizations of such systems are given by random matrices expressed in a block form where the terms responsible for the quench dynamics are the off-diagonal blocks. Our analysis examines both dense and sparse random matrix realizations of the Hamiltonians and the observables. Sparse random matrices may be associated with local quantum Hamiltonians and they show a different spread of the observables on the energy eigenstates with respect to the dense ones. In particular, the numerical data seems to support the existence of rare states, i.e. states where the observables take expectation values which are different compared to the typical ones sampled by the micro-canonical distribution. In the case of sparse random matrices we also extract the finite size behavior of two different time scales associated with the thermalization process.