Percolation-enhanced localization in the disordered bosonic hubbard model

Abstract

We present a new (mean-field-RPA) study of the bosonic Hubbard model with chemical-potential disorder Δ at zero temperature. We get the fractional-filling phase diagram by monitoring site-dependent superfluid order parameters ψ_i and fillings n_i. Our theory suggests a new physical picture for the superfluid-Bose glass transition, as a localization transition enhanced by the percolation of sites with negligible ψ_i at a critical Δ_c: for Δ>Δ_c sites with substantial ψ_i's percolate across the lattice; for Δ<Δ_c this percolation stops. This picture, though only approximately correct especially in low dimensions, should be relevant for Monte Carlo studies of the disordered bosonic Hubbard model.