Signatures of the Many-body Localized Regime in Two Dimensions

TL;DR

This paper presents the first large-scale numerical study of many-body localization in a two-dimensional disordered Bose-Hubbard model, revealing entanglement signatures and a phase transition consistent with experimental observations.

Contribution

It introduces a generalized low-depth quantum circuit method for approximating eigenstates in 2D, enabling analysis beyond traditional exact diagonalization techniques.

Findings

Entanglement entropy fluctuations peak at the localization transition.

Eigenstate entanglement structure indicates a phase transition.

Results align with experimental data on 2D many-body localization.

Abstract

Lessons from Anderson localization highlight the importance of dimensionality of real space for localization due to disorder. More recently, studies of many-body localization have focussed on the phenomenon in one dimension using techniques of exact diagonalization and tensor networks. On the other hand, experiments in two dimensions have provided concrete results going beyond the previously numerically accessible limits while posing several challenging questions. We present the first large-scale numerical examination of a disordered Bose-Hubbard model in two dimensions realized in cold atoms, which shows entanglement based signatures of many-body localization. By generalizing a low-depth quantum circuit to two dimensions we approximate eigenstates in the experimental parameter regimes for large systems, which is beyond the scope of exact diagonalization. A careful analysis of the eigenstate entanglement structure provides an indication of the putative phase transition marked by a peak in the fluctuations of entanglement entropy in a parameter range consistent with experiments.