Variational cluster approach for strongly correlated lattice bosons in the superfluid phase

TL;DR

This paper extends the variational cluster approach to strongly correlated lattice bosons in the superfluid phase, reformulating it with a pseudoparticle formalism and applying it to the 2D Bose-Hubbard model, achieving results consistent with quantum Monte Carlo.

Contribution

The paper introduces a pseudoparticle formalism within the variational cluster approach for superfluid bosons, enabling accurate analysis of the Bose-Hubbard model.

Findings

Results agree well with quantum Monte Carlo simulations.

The method accurately captures both Mott and superfluid phases.

Provides expressions for key physical quantities like Green's functions and condensate density.

Abstract

We extend the variational cluster approach to deal with strongly correlated lattice bosons in the superfluid phase. To this end, we reformulate the approach within a pseudoparticle formalism, whereby cluster excitations are described by particlelike excitations. The approximation amounts to solving a multicomponent noninteracting bosonic system by means of a multimode Bogoliubov approximation. A source-and-drain term is introduced in order to break U(1) symmetry at the cluster level. We provide an expression for the grand potential, the single-particle normal and anomalous Green's functions, the condensate density, and other static quantities. As a first nontrivial application of the method we choose the two-dimensional Bose-Hubbard model and evaluate results in both the Mott and the superfluid phases. Our results show an excellent agreement with quantum Monte Carlo calculations.