Coexistence of localization and transport in many-body two-dimensional Aubry-Andr\'e models

TL;DR

This study demonstrates that two-dimensional quasiperiodic Aubry-André models can exhibit a long-lived many-body localized phase alongside large-scale transport, revealing coexistence of localization and transport phenomena.

Contribution

It provides the first evidence of coexisting localization and transport in 2D quasiperiodic many-body systems, contrasting with disordered systems where rare regions induce thermalization.

Findings

Long-lived MBL phase observed in 2D quasiperiodic models

Deterministic weak potential lines support large-scale transport

Coexistence of localization and transport akin to supersolids

Abstract

Whether disordered and quasiperiodic many-body quantum systems host a long-lived localized phase in the thermodynamic limit has been the subject of intense recent debate. While in one dimension substantial evidence for the existence of such a many-body localized (MBL) phase exists, the behavior in higher dimensions remains an open puzzle. In two-dimensional disordered systems, for instance, it has been argued that rare regions may lead to thermalization of the whole system through a mechanism dubbed the avalanche instability. In quasiperiodic systems, rare regions are altogether absent and the fate of a putative many-body localized phase has hitherto remained largely unexplored. In this work, we investigate the localization properties of two many-body quasiperiodic models, which are two-dimensional generalizations of the Aubry-Andr\'e model. By studying the out-of-equilibrium dynamics of large systems, we find a long-lived MBL phase, in contrast to random systems. Furthermore, we show that deterministic lines of weak potential, which appear in investigated quasiperiodic models, support large-scale transport, while the system as a whole does not thermalize. Our results demonstrate that quasiperiodic many-body systems have the remarkable and counter-intuitive capability of exhibiting coexisting localization and transport properties - a phenomenon reminiscent of the behavior of supersolids. Our findings are of direct experimental relevance and can be tested, for instance, using state-of-the-art cold atomic systems.