Entropy of isolated quantum systems after a quench

TL;DR

This paper investigates the diagonal entropy in isolated quantum systems after a quench, demonstrating its relation to thermalization in chaotic regimes and its behavior in integrable systems, highlighting differences from generalized Gibbs ensembles.

Contribution

It introduces the behavior of diagonal entropy in different quantum regimes post-quench, clarifying its relation to thermalization and integrability.

Findings

Diagonal entropy aligns with microcanonical entropy in chaotic systems.

In integrable systems, diagonal entropy is additive but differs from generalized Gibbs ensemble entropy.

Diagonal entropy provides insight into thermalization processes in quantum quenches.

Abstract

A diagonal entropy, which depends only on the diagonal elements of the system's density matrix in the energy representation, has been recently introduced as the proper definition of thermodynamic entropy in out-of-equilibrium quantum systems. We study this quantity after an interaction quench in lattice hard-core bosons and spinless fermions, and after a local chemical potential quench in a system of hard-core bosons in a superlattice potential. The former systems have a chaotic regime, where the diagonal entropy becomes equivalent to the equilibrium microcanonical entropy, coinciding with the onset of thermalization. The latter system is integrable. We show that its diagonal entropy is additive and different from the entropy of a generalized Gibbs ensemble, which has been introduced to account for the effects of conserved quantities at integrability.