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

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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 Green's function. An appropriate functional is derived, which is stationary at the exact physical realization 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 proposed in Phys. Rev. B 83, 134507 (2011). We present results for the superfluid density in the two-dimensional Bose-Hubbard model, which shows a remarkable agreement with those of quantum-Monte-Carlo calculations.
Original languageEnglish
Pages (from-to)014535
Number of pages1
JournalPhysical review / E
Volume84
Issue number1
DOIs
Publication statusPublished - 1 Jul 2011

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Superfluid
Energy Functional
Bosons
bosons
Superfluidity
Quantum Monte Carlo
Bose-Einstein Condensation
Hubbard Model
Local Interaction
Functional Integral
Condensate
Legendre
Numerical Techniques
Energy
Integral Representation
Order Parameter
energy
Green's function
Physics
Legendre functions

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Extended self-energy functional approach for strongly correlated lattice bosons in the superfluid phase. / Arrigoni, Enrico; Knap, Michael; von der Linden, Wolfgang.

In: Physical review / E, Vol. 84, No. 1, 01.07.2011, p. 014535.

Research output: Contribution to journalArticleResearchpeer-review

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