Quantum Quenches, Thermalization and Many-Body Localization

TL;DR

This paper explores the connection between thermalization after a quantum quench and many-body delocalization in strongly correlated systems, using numerical simulations on an anisotropic Heisenberg spin chain.

Contribution

It provides numerical evidence linking thermalization to many-body delocalization, emphasizing the role of homogeneous integrability-breaking terms in ergodicity.

Findings

Thermalization correlates with many-body delocalization in quasiparticle space.

Homogeneous integrability-breaking promotes ergodicity and thermalization.

Level spacing statistics and eigenstate analysis support the conjecture.

Abstract

We conjecture that thermalization following a quantum quench in a strongly correlated quantum system is closely connected to many-body delocalization in the space of quasi-particles. This scenario is tested in the anisotropic Heisenberg spin chain with different types of integrability-breaking terms. We first quantify the deviations from integrability by analyzing the level spacing statistics and the inverse participation ratio of the system's eigenstates. We then focus on thermalization, by studying the dynamics after a sudden quench of the anisotropy parameter. Our numerical simulations clearly support the conjecture, as long as the integrability-breaking term acts homogeneously on the quasiparticle space, in such a way as to induce ergodicity over all the relevant Hilbert space.