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

TL;DR

This paper introduces a high-order perturbative diagrammatic process chain method to analyze the ground state and phase diagram of the Bose-Hubbard model across various dimensions and fillings, achieving high accuracy in phase boundary determination.

Contribution

The paper develops a numerically straightforward, high-order perturbation technique based on Kato's series for the Bose-Hubbard model, enabling detailed ground-state and phase boundary analysis.

Findings

Computed ground-state energies and correlations for 1D, 2D, 3D lattices.

Discovered a scaling behavior reducing dependence on filling factor.

Accurately determined the Mott insulator to superfluid phase boundary.

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.