Green's function approach to the Bose-Hubbard model with disorder

TL;DR

This paper develops a Green's function approach to analyze the phase diagram of the disordered Bose-Hubbard model, distinguishing superfluid, Mott-insulator, and Bose-glass phases with improved accuracy over mean-field methods.

Contribution

It introduces a diagrammatic hopping expansion for the finite-temperature Green's function to accurately identify phase boundaries and characterize low-energy excitations in disordered bosonic systems.

Findings

Derived phase diagram for bounded on-site disorder.

Established criteria for phase identification beyond mean-field theory.

Calculated local correlations and density of states for different phases.

Abstract

We analyse the distinction between the three different ground states presented by a system of spinless bosons with short-range interactions submitted to a random potential using the disordered Bose-Hubbard model. The criteria for identifying the superfluid, the Mott-insulator, and the Bose-glass phases at finite temperatures are discussed for small values of the kinetic energy associated with the tunnelling of particles between potential wells. Field theoretical considerations are applied in order to construct a diagrammatic hopping expansion to the finite-temperature Green's function. By performing a summation of subsets of diagrams we are able to find the condition to the long-range correlations which leads to the phase boundary between superfluid and insulating phases. The perturbative expression to the local correlations allows us to calculate an approximation to the single-particle density of states of low-energy excitations in the presence of small hopping, which characterizes unambiguously the distinction between the Mott-insulator and the Bose-glass phases. We obtain the phase diagram for bounded on-site disorder. It is demonstrated that our analysis is capable of going beyond the mean-field theory results for the classification of these different ground states.