Stochastic Mean-Field Theory for the Disordered Bose-Hubbard Model

TL;DR

This paper introduces a stochastic mean-field theory for the disordered Bose-Hubbard model that effectively captures localization effects and predicts a critical hopping strength for superfluidity despite strong disorder.

Contribution

It presents a novel stochastic mean-field approach that overcomes finite-size limitations and describes the Bose glass phase in disordered bosonic systems.

Findings

Existence of a critical hopping strength for superfluidity.

The new method captures localization effects beyond traditional mean-field.

Superfluid phase persists at arbitrary disorder levels above the critical hopping.

Abstract

We investigate the effect of diagonal disorder on bosons in an optical lattice described by an Anderson-Hubbard model at zero temperature. It is known that within Gutzwiller mean-field theory spatially resolved calculations suffer particularly from finite system sizes in the disordered case, while arithmetic averaging of the order parameter cannot describe the Bose glass phase for finite hopping $J>0$. Here we present and apply a new \emph{stochastic} mean-field theory which captures localization due to disorder, includes non-trivial dimensional effects beyond the mean-field scaling level and is applicable in the thermodynamic limit. In contrast to fermionic systems, we find the existence of a critical hopping strength, above which the system remains superfluid for arbitrarily strong disorder.