Improving Mean-Field Theory for Bosons in Optical Lattices via Degenerate Perturbation Theory

Abstract

The objective of this paper is the theoretical description of the Mott-insulator to superfluid quantum phase transition of a Bose gas in an optical lattice. In former works the Rayleigh-Schrödinger perturbation theory was used within a mean-field approach, which yields partially non-physical results since the degeneracy between two adjacent Mott lobes is not taken into account. In order to correct such non-physical results we apply the Brillouin-Wigner perturbation theory to the mean-field approximation of the Bose-Hubbard model. Detailed explanations of how to use the Brillouin-Wigner theory are presented, including a graphical approach that allows to efficiently keep track of the respective analytic terms. To prove the validity of this computation, the results are compared with other works. Besides the analytic calculation of the phase boundary from Mott-insulator to superfluid phase, the condensate density is also determined by simultaneously solving two algebraic equations. The analytical and numerical results turn out to be physically meaningful and can cover a region of system parameters inaccessible until now. Our results are of particular interest provided an harmonic trap is added to the former calculations in an homogeneous system, in view of describing an experiment within the local density approximation. Thus, the paper represents an essential preparatory work for determining the experimentally observed wedding-cake structure of particle-density profile at both finite temperature and hopping.

References in corpus (19)

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• Cold bosonic atoms in optical lattices
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• Bosonic self-energy functional theory
• High-order symbolic strong-coupling expansion for the Bose-Hubbard model
• Perturbative calculation of critical exponents for the Bose-Hubbard model

Cited by in corpus (7)

• Beyond hard-core bosons in transmon arrays
• Phases and collective modes of bosons in a triangular lattice at finite temperature: A cluster mean field study
• Ultracold Bosons on a Regular Spherical Mesh
• Finite-temperature degenerate perturbation theory for bosons in optical lattices
• Strong-coupling RPA theory of a Bose gas near the superfluid--Mott-insulator transition: universal thermodynamics and two-body contact
• Two-body contact of a Bose gas near the superfluid--Mott-insulator transition
• Extended Bose-Hubbard Model on Small Grids: Exact Diagonalization and Monte Carlo Studies