Process chain approach to the Bose-Hubbard model: Ground-state properties and phase diagram

Abstract

We carry out a perturbative analysis, of high order in the tunneling parameter, of the ground state of the homogeneous Bose-Hubbard model in the Mott insulator phase. This is made possible by a diagrammatic process chain approach, derived from Kato's representation of the many-body perturbation series, which can be implemented numerically in a straightforward manner. We compute ground-state energies, atom-atom correlation functions, density-density correlations, and occupation number fluctuations, for one-, two-, and three-dimensional lattices with arbitrary integer filling. A phenomenological scaling behavior is found which renders the data almost independent of the filling factor. In addition, the process chain approach is employed for calculating the boundary between the Mott insulator phase and the superfluid phase with high accuracy. We also consider systems with dimensionalities d>3, thus monitoring the approach to the mean-field limit. The versatility of the method suggests further applications to other systems which are less well understood.

15 pages, 20 figures

References in corpus (8)

• Many-Body Physics with Ultracold Gases
• Quantum Monte Carlo simulations of confined bosonic atoms in optical lattices
• Interference pattern and visibility of a Mott insulator
• Spatial correlations of trapped 1d bosons in an optical lattice
• Strong-coupling expansion for the momentum distribution of the Bose Hubbard model with benchmarking against exact numerical results
• Quantum Many-Body Dynamics of Coupled Double-Well Superlattices
• Bose-Hubbard phase diagram with arbitrary integer filling
• Process chain approach to high-order perturbation calculus for quantum lattice models