Many-body localization in a tilted potential in two dimensions

TL;DR

This paper explores how a linear potential affects thermalization in a two-dimensional many-body system, finding that stronger gradients are needed to prevent thermalization compared to one dimension, with implications for experimental observations.

Contribution

It extends the study of Stark many-body localization to two dimensions, analyzing the conditions under which localization persists or breaks down.

Findings

Stronger potential gradients are required to inhibit thermalization in 2D.

Density-polarized regions act as bottlenecks for transport.

Delocalization is generally favored in 2D systems, but nonergodic states can still occur.

Abstract

Thermalization in many-body systems can be inhibited by the application of a linearly increasing potential, which is known as Stark many-body localization. Here we investigate the fate of this phenomenon on a two-dimensional disorder-free lattice with up to $24 \times 6$ sites. Similar to the one-dimensional case, "density-polarized" regions can act as bottlenecks for transport and thermalization on laboratory timescales. However, compared to the one-dimensional case, a substantially stronger potential gradient is needed to prevent thermalization when an extra spatial dimension is involved. The origin of this difference and implications for experiments are discussed. We argue that delocalization is generally favored for typical states in two-dimensional Stark many-body systems, although nonergodicity can still be observed for a specific choice of initial states, such as those probed in experiments.