Non-existence of Bose-Einstein condensation in Bose-Hubbard model in dimensions 1 and 2

TL;DR

This paper proves that Bose-Einstein condensation cannot occur in the Bose-Hubbard model in one and two dimensions at any nonzero temperature, using the Bogoliubov inequality.

Contribution

It demonstrates the non-existence of Bose-Einstein condensation in low-dimensional Bose-Hubbard models, extending classical continuum results to lattice systems.

Findings

Bose-Einstein condensation is ruled out in 1D and 2D Bose-Hubbard models.

The result applies at any filling and nonzero temperature.

The proof uses the Bogoliubov inequality.

Abstract

We apply the Bogoliubov inequality to the Bose-Hubbard model to rule out the possibility of Bose-Einstein condensation. The result holds in one and two dimensions, for any filling at any nonzero temperature. This result can be considered as complementary to analogous, classical result known for interacting bosons in continuum.