Stochastic Mean-Field Theory: Method and Application to the Disordered Bose-Hubbard Model at Finite Temperature and Speckle Disorder

TL;DR

This paper introduces the stochastic mean-field theory (SMFT) for disordered Bose systems, applying it to the disordered Bose-Hubbard model at finite temperature with various disorder types, revealing disorder effects on condensation and phase behavior.

Contribution

The paper develops and details the SMFT method for disordered Bose systems, extending its application to finite temperature and speckle disorder, including off-diagonal hopping disorder effects.

Findings

Disorder-induced condensation occurs only at low temperatures.

Reentrant behavior at constant filling is observed at low temperatures.

SMFT combined with LDA predicts condensate fraction under trapping potentials.

Abstract

We discuss the stochastic mean-field theory (SMFT) method which is a new approach for describing disordered Bose systems in the thermodynamic limit including localization and dimensional effects. We explicate the method in detail and apply it to the disordered Bose-Hubbard model at finite temperature, with on-site box disorder, as well as experimentally relevant unbounded speckle disorder. We find that disorder-induced condensation and reentrant behavior at constant filling are only possible at low temperatures, beyond the reach of current experiments [Pasienski et al., arXiv:0908.1182]. Including off-diagonal hopping disorder as well, we investigate its effect on the phase diagram in addition to pure on-site disorder. To make contact to present experiments on a quantitative level, we also combine SMFT with an LDA approach and obtain the condensate fraction in the presence of an external trapping potential.