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

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.

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

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• Realizing Topological Superconductivity in Tunable Bose-Fermi Mixtures with Transition Metal Dichalcogenide Heterostructures
• Nonequilibrium self-energy functional theory
• Variational cluster approach to the single impurity Anderson model
• Bosonic self-energy functional theory
• Variational Cluster Approximation to the Thermodynamics of Quantum Spin Systems
• Optical Response in Excitonic Insulating State: Variational Cluster Approach
• Quantum density anomaly in optically trapped ultracold gases
• Bose-Hubbard model with occupation-parity couplings
• Self-energy functional theory with symmetry breaking for disordered lattice bosons
• Strong-coupling RPA theory of a Bose gas near the superfluid--Mott-insulator transition: universal thermodynamics and two-body contact
• The infinite occupation number basis of bosons - solving a numerical challenge
• Non-equilibrium variational cluster perturbation theory: quench dynamics of the quantum Ising model