Extended self-energy functional approach for strongly-correlated lattice bosons in the superfluid phase

TL;DR

This paper extends the self-energy functional approach to include superfluidity in strongly correlated lattice bosons, enabling non-perturbative analysis of superfluid phases with results matching Quantum Monte Carlo data.

Contribution

The authors develop an extended self-energy functional approach that incorporates superfluidity, overcoming previous limitations of the SFA for Bose-Einstein condensates.

Findings

Accurate superfluid density results for 2D Bose-Hubbard model

Method is non-perturbative and widely applicable

Equivalence to pseudoparticle approach established

Abstract

Among the various numerical techniques to study the physics of strongly correlated quantum many-body systems, the self-energy functional approach (SFA) has become increasingly important. In its previous form, however, SFA is not applicable to Bose-Einstein condensation or superfluidity. In this paper we show how to overcome this shortcoming. To this end we identify an appropriate quantity, which we term $D$, that represents the correlation correction of the condensate order parameter, as it does the self-energy for the Green's function. An appropriate functional is derived, which is stationary at the exact physical realizations of $D$ and of the self-energy. Its derivation is based on a functional-integral representation of the grand potential followed by an appropriate sequence of Legendre transformations. The approach is not perturbative and therefore applicable to a wide range of models with local interactions. We show that the variational cluster approach based on the extended self-energy functional is equivalent to the "pseudoparticle" approach introduced in Phys. Rev. B, 83, 134507 (2011). We present results for the superfluid density in the two-dimensional Bose-Hubbard model, which show a remarkable agreement with those of Quantum-Monte-Carlo calculations.