Many body localization and delocalization in the two dimensional continuum

TL;DR

This paper investigates the stability of many-body localization in two-dimensional continuum systems with short-range interactions, finding it stable below a critical temperature but generally unstable in speckle disorder scenarios.

Contribution

It provides a detailed analysis of the conditions under which many-body localization can persist in 2D continuum systems, including the effects of temperature and disorder type.

Findings

Localization is stable below a critical temperature $T_c$ for impurity models.

Perturbation theory diverges for speckle disorder, indicating delocalization.

The stability boundary depends on interaction strength and temperature.

Abstract

I discuss whether localization in the two dimensional continuum can be stable in the presence of short range interactions. I conclude that, for an impurity model of disorder, if the system is prepared below a critical temperature $T < T_c$, then perturbation theory about the localized phase converges almost everywhere. As a result, the system is at least asymptotically localized, and perhaps even truly many body localized, depending on how certain rare regions behave. Meanwhile, for $T > T_c$, perturbation theory fails to converge, which I interpret as interaction mediated delocalization. I calculate the boundary of the region of perturbative stability of localization in the interaction strength - temperature plane. I also discuss the behavior in a speckle disorder (relevant for cold atoms experiments) and conclude that perturbation theory about the non-interacting phase diverges for arbitrarily weak interactions with speckle disorder, suggesting that many body localization in the two dimensional continuum cannot survive away from the impurity limit.