Thermodynamics of the Bose-Hubbard model in a Bogoliubov+U theory

TL;DR

This paper introduces the Bogoliubov+U formalism to accurately analyze the thermodynamics of the Bose-Hubbard model, extending mean-field approaches with a variational self-energy method.

Contribution

The paper develops a new Bogoliubov+U framework that effectively captures thermodynamic properties and phase diagrams of the Bose-Hubbard model with high accuracy.

Findings

Reproduces T=0 phase diagrams with 1% accuracy

Accurately models superfluid to normal transition at finite temperature

Provides a self-consistent, parameter-efficient theoretical approach

Abstract

We derive the Bogoliubov+U formalism to study the thermodynamical properties of the Bose-Hubbard model. The framework can be viewed as the zero-frequency limit of bosonic dynamical mean-field theory (B-DMFT), but equally well as an extension of the mean-field decoupling approximation in which pair creation and annihilation of depleted particles is taken into account. The self-energy on the impurity site is treated variationally, minimizing the grand potential. The theory containing just three parameters that are determined self-consistently reproduces the T=0 phase diagrams of the three-dimensional and two-dimensional Bose-Hubbard model with an accuracy of 1% or better. The superfluid to normal transition at finite temperature is also reproduced well and only slightly less accurately than in B-DMFT.