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

We study Bose–Einstein Condensation (BEC) in the Infinite-Range-Hopping Bose–Hubbard model with repulsive on-site particle interaction in the presence of an ergodic random single-site external potential with different distributions. We show that the model is exactly soluble even if the on-site interaction is random. We observe 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 certain fractional densities. We show that this suppression appears with increasing disorder. On the other hand, the suppression of BEC at integer densities observed in Bru and Dorlas (J. Stat. Phys. 113:177–195, 2003) in the absence of a random potential, can disappear as the 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 the density for large repulsion. Again, the threshold for this repulsion gets higher, when disorder increases.