Dynamics of Negativity of a Wannier-Stark Many-Body Localized System Coupled to a Bath

TL;DR

This paper studies how entanglement evolves in a Wannier-Stark many-body localized system when coupled to an environment, using the third Rényi negativity to distinguish localized phases and quantify quantum correlations.

Contribution

It introduces the use of third Rényi negativity as a tool to analyze entanglement dynamics in Wannier-Stark MBL systems coupled to a bath, highlighting its ability to detect localization.

Findings

Logarithmic growth of entanglement in intermediate times

Distinguishes Wannier-Stark MBL from non-interacting localization

Quantifies quantum correlations in mixed states

Abstract

An interacting system subjected to a strong linear potential can host a many-body localized (MBL) phase when being slightly perturbed. This so-called Wannier-Stark or `tilted-field' MBL phase inherits many properties from the well-investigated disordered MBL phase, and provides an alternative route to experimentally engineer interacting localized systems without quenched disorder. In this work, we investigate the dynamics of entanglement in a Wannier-Stark MBL system coupled to a dephasing environment. As an accessible entanglement proxy, we use the third R\'{e}nyi negativity $R_3$, which reduces to the third R\'{e}nyi entropy in case the system is isolated from the environment. This measure captures the characteristic logarithmic growth of interacting localized phases in the intermediate-time regime, where the effects of the coupling to the environment are not yet dominating the dynamics. Thus it forms a tool to distinguish Wannier-Stark MBL from non-interacting Wannier-Stark localization up to intermediate time-scales, and to quantify quantum correlations in mixed-state dynamics.