Mobility edge of the two dimensional Bose-Hubbard model

TL;DR

This paper investigates the localization transition in the two-dimensional Bose-Hubbard model under disorder, revealing a mobility edge that decays exponentially with disorder strength and exhibits weak multi-fractality at criticality.

Contribution

It introduces a fluctuation operator expansion method to analyze the quasiparticle spectrum and identifies a disorder-driven mobility edge with specific scaling and critical properties.

Findings

Mobility edge decays exponentially with disorder strength

Localization exhibits weak multi-fractality at the transition

Finite-size scaling matches experimental observations

Abstract

We analyze the disorder driven localization of the two dimensional Bose-Hubbard model by evaluating the full low energy quasiparticle spectrum via a recently developed fluctuation operator expansion method. For any strength of the local interaction we find a mobility edge that displays an approximately exponential decay with increasing disorder strength. We determine the finite-size scaling collapse and exponents at this critical line finding that the localization of excitations is characterized by weak multi-fractality and a thermal-like critical gap ratio. A direct comparison to a recent experiment yields an excellent match of the predicted finite-size transition point and scaling of single particle correlations.