The Bogoliubov-Bose-Hubbard model: existence of minimizers and absence of quantum phase transition

TL;DR

This paper uses a variational approach based on Bogoliubov theory to analyze the Bose-Hubbard model, proving the existence of minimizers and demonstrating a thermal phase transition without a quantum phase transition.

Contribution

It introduces a variational framework for the Bose-Hubbard model and establishes the absence of quantum phase transitions while confirming thermal phase transitions.

Findings

Existence of minimizers for free energy functionals

Thermally driven superfluid to insulator transition

No quantum phase transition observed in the model

Abstract

We consider a variational approach to the Bose-Hubbard model based on Bogoliubov theory. We introduce the grand canonical and canonical free energy functionals for which we prove the existence of minimizers. By analyzing their structure we show the existence of a thermally driven phase transition by showing that the system is superfluid at sufficiently low temperatures and insulating at high temperatures. In particular, we show that this model does not exhibit a quantum phase transition.