C^*-algebraic approach to the Bose-Hubbard model

TL;DR

This paper introduces a new algebraic derivation of the pressure formula for the long-range Bose-Hubbard model, extending noncommutative large deviation techniques and proving Bose-Einstein condensation at small coupling.

Contribution

It provides a novel algebraic approach to derive the pressure formula and extends the method to more general Bose systems of mean-field type.

Findings

Derived a new variational formula for the pressure.

Extended noncommutative large deviation techniques to Bose systems.

Proved Bose-Einstein condensation for small coupling cases.

Abstract

We give a new derivation of the variational formula for the pressure of the long-range-hopping Bose-Hubbard model, which was first proved in \cite{BD}. The proof is analogous to that of a theorem on noncommutative large deviations introduced by Petz, Raggio and Verbeure \cite{PRV} and could similarly be extended to more general Bose system of mean-field type. We apply this formalism to prove Bose-Einstein condensation for the case of small coupling.