Strong-coupling expansion for the momentum distribution of the Bose Hubbard model with benchmarking against exact numerical results

Abstract

A strong-coupling expansion for the Green's functions, self-energies and correlation functions of the Bose Hubbard model is developed. We illustrate the general formalism, which includes all possible inhomogeneous effects in the formalism, such as disorder, or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third-order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator to superfluid transition along with a generalization of the RPA-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions; the accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling theory results are benchmarked against numerically exact QMC simulations in two and three dimensions and against DMRG calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.

arXiv comment48 pages 14 figures RevTeX

References in corpus (20)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Cold bosonic atoms in optical lattices
• Quantum Monte Carlo with Directed Loops
• The Mott insulator transition in two dimensions
• The one-dimensional Bose-Hubbard Model with nearest-neighbor interaction
• Strong-coupling expansions for the pure and disordered bose Hubbard model
• Phases of the one-dimensional Bose-Hubbard model
• Monte Carlo study of two-dimensional Bose-Hubbard model
• Phase diagram of the bose Hubbard model
• Formation of spatial shell structures in the superfluid to Mott insulator transition
• Dynamics and Thermodynamics of the Bose-Hubbard model
• Mott insulator to superfluid transition in the Bose-Hubbard model: a strong-coupling approach
• Condensate fraction in a 2D Bose gas measured across the Mott-insulator transition
• Recent Developments of World-Line Monte Carlo Methods
• Spatial correlations of trapped 1d bosons in an optical lattice
• Expansion of a quantum gas released from an optical lattice
• Spectral weight redistribution in strongly correlated bosons in optical lattices
• Bose-Hubbard phase diagram with arbitrary integer filling
• The Mott insulator phase of the one dimensional Bose-Hubbard model: a high order perturbative study
• Dirty Bosons: Twenty Years Later

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