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

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

2011-03-18

arxiv.org/abs/1103.3664v3

Phys. Rev. B 84, 014535 (2011)

Physics

Condensed Matter

Quantum Gases

1 additional figure showing the region close to the tip of the Mott lobe, minor changes in the text

Scientific paper

10.1103/PhysRevB.84.014535

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.

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