Gutzwiller approach to the Bose-Hubbard model with random local impurities

TL;DR

This paper uses a Gutzwiller approach to analyze the phase diagram of a disordered Bose-Hubbard model with binary local potentials, revealing phases with varying compressibility and superfluid properties in ultracold atom systems.

Contribution

It introduces a site-dependent Gutzwiller method to study disordered Bose-Hubbard models, providing analytical insights into phase behavior with binary disorder in one- and two-dimensional lattices.

Findings

Agreement with previous results on compressibility

Identification of peaks in excitation spectrum related to incompressible phases

Discovery of superfluid character in partially compressible phases

Abstract

Recently it has been suggested that fermions whose hopping amplitude is quenched to extremely low values provide a convenient source of local disorder for lattice bosonic systems realized in current experiment on ultracold atoms. Here we investigate the phase diagram of such systems, which provide the experimental realization of a Bose-Hubbard model whose local potentials are randomly extracted from a binary distribution. Adopting a site-dependent Gutzwiller description of the state of the system, we address one- and two-dimensional lattices and obtain results agreeing with previous findings, as far as the compressibility of the system is concerned. We discuss the expected peaks in the experimental excitation spectrum of the system, related to the incompressible phases, and the superfluid character of the {\it partially compressible phases} characterizing the phase diagram of systems with binary disorder. In our investigation we make use of several analytical results whose derivation is described in the appendices, and whose validity is not limited to the system under concern.