Stable many-body localization under random continuous measurements in the no-click limit

TL;DR

This study explores how many-body localization persists under continuous random measurements in a non-Hermitian setting, revealing enhanced localization effects and size-dependent transition behavior through numerical and analytical methods.

Contribution

It extends the quantum random energy model to non-Hermitian scenarios, demonstrating stronger localization and altered transition scaling in the presence of random gain and loss.

Findings

Localization persists for any finite disorder

Non-Hermitian QREM shows stronger localization effects

Transition scaling differs from Hermitian case, W_c ~ ln^{1/2} L

Abstract

In this work, we investigate the localization properties of a paradigmatic model, coupled to a monitoring environment and possessing a many-body localized (MBL) phase. We focus on the post-selected no-click limit with quench random rates, i.e., random gains and losses. In this limit, the system is modeled by adding an imaginary random potential, rendering non-Hermiticity in the system. Numerically, we provide an evidence that the system is localized for any finite amount of disorder. To analytically understand our results, we extend the quantum random energy model (QREM) to the non-Hermitian scenario. The Hermitian QREM has been used previously as a benchmark model for MBL. The QREM exhibits a size-dependent MBL transition, where the critical value scales as $W_c\sim \sqrt{L} \ln{L}$ with system size and presenting many-body mobility edges. We reveal that the non-Hermitian QREM with random gain-loss offers a significantly stronger form of localization, evident in the nature of the many-body mobility edges and the value for the transition, which scales as $W_c\sim \ln^{1/2}{L}$ with the system size.