Out-of-equilibrium Correlated Systems : Bipartite Entanglement as a Probe of Thermalization

TL;DR

This paper investigates how bipartite entanglement measures can serve as indicators of thermalization in out-of-equilibrium quantum systems, using a quench in the XXZ spin chain as a case study.

Contribution

It introduces a novel bipartition preserving translation symmetry to analyze entanglement spectra, revealing differences between integrable and non-integrable regimes in thermalization behavior.

Findings

Entanglement entropy quickly reaches a plateau after a quench.

In integrable chains, entanglement spectra show persistent fluctuations.

Breaking integrability aligns entanglement spectra with thermal predictions.

Abstract

Thermalization play a central role in out-of-equilibrium physics of ultracold atoms or electronic transport phenomena. On the other hand, entanglement concepts have proven to be extremely useful to investigate quantum phases of matter. Here, it is argued that **bipartite** entanglement measures provide key information on out-of-equilibrium states and might therefore offer stringent thermalization criteria. This is illustrated by considering a global quench in an (extended) XXZ spin-1/2 chain across its (zero-temperature) quantum critical point. A non-local **bipartition** of the chain **preserving translation symmetry** is proposed. The time-evolution after the quench of the **reduced** density matrix of the half-system is computed and its associated (time-dependent) entanglement spectrum is analyzed. Generically, the corresponding entanglement entropy quickly reaches a "plateau" after a short transient regime. However, in the case of the integrable XXZ chain, the low-energy entanglement spectrum still reveals strong time-fluctuations. In addition, its infinite-time average shows strong deviations from the spectrum of a Boltzmann thermal density matrix. In contrast, when the integrability of the model is broken (by small next-nearest neighbor couplings), the entanglement spectra of the time-average and thermal density matrices become remarkably similar.