Variational Cluster Perturbation Theory for Bose-Hubbard models

TL;DR

This paper applies variational cluster perturbation theory to the Bose-Hubbard model, accurately capturing the phase transition and excitation spectrum, and demonstrating good agreement with established numerical methods.

Contribution

It introduces a formulation of VCPT that preserves translation invariance in the excitation spectrum and accurately reproduces phase diagrams for Bose-Hubbard models.

Findings

VCPT yields a translation-invariant excitation spectrum.

The phase diagram matches density-matrix renormalization group results.

Good quantitative agreement for clusters of about 10 sites.

Abstract

We discuss the application of the variational cluster perturbation theory (VCPT) to the Mott-insulator--to--superfluid transition in the Bose-Hubbard model. We show how the VCPT can be formulated in such a way that it gives a translation invariant excitation spectrum -- free of spurious gaps -- despite the fact that if formally breaks translation invariance. The phase diagram and the single-particle Green function in the insulating phase are obtained for one-dimensional systems. When the chemical potential of the cluster is taken as a variational parameter, the VCPT reproduces the dimension dependence of the phase diagram even for one-site clusters. We find a good quantitative agreement with the results of the density-matrix renormalization group when the number of sites in the cluster becomes of order 10. The extension of the method to the superfluid phase is discussed.