Condensation in a Disordered Infinite-Range Hopping Bose-Hubbard Model

TL;DR

This paper analyzes how disorder affects Bose-Einstein Condensation in an infinite-range hopping Bose-Hubbard model, revealing suppression phenomena and the influence of disorder on critical temperature and density.

Contribution

It provides an exact solution for the disordered model and uncovers new disorder-induced suppression effects on BEC not seen in the non-random case.

Findings

Disorder can suppress BEC at certain densities.

Suppression of BEC diminishes at integer densities with increasing disorder.

Critical temperature decreases with small on-site repulsion and disorder.

Abstract

We study Bose-Einstein Condensation (BEC) in the Infinite-Range Hopping Bose-Hubbard model for repulsive on-site particle interaction in presence of ergodic random one-site potentials with different distributions. We show that the model is exactly soluble even if the on-site interaction is random. But in contrast to the non-random case, we observe here new phenomena: instead of enhancement of BEC for perfect bosons, for constant on-site repulsion and discrete distributions of the single-site potential there is suppression of BEC at some fractional densities. We show that this suppression appears with increasing disorder. On the other hand, the BEC suppression at integer densities may disappear, if disorder increases. For a continuous distribution we prove that the BEC critical temperature decreases for small on-site repulsion while the BEC is suppressed at integer values of density for large repulsion. Again, the threshold for this repulsion gets higher, when disorder increases.