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

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.

12 pages, 5 figures. Some adjustments made to the manuscript and to figures. A few relevant observations added throughout the manuscript. Bibliography made more compact (collapsed some items)

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• Superfluidity of Interacting Bosonic Mixtures in Optical Lattices
• Phase diagram of the disordered Bose-Hubbard model
• The Dissipative Bose-Hubbard Model. Methods and Examples
• Equilibration Dynamics of Strongly Interacting Bosons in 2D Lattices with Disorder
• Superfluid clusters, percolation and phase transitions in the disordered, two dimensional Bose-Hubbard model
• Dynamics of Disordered States in the Bose-Hubbard Model with Confinement
• The Mean-Field Bose Glass in Quasicrystalline Systems
• Quantitative study of two- and three-dimensional strong localization of matter waves by atomic scatterers
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