Percolation-Enhanced Localization in the Disordered Bosonic Hubbard Model

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 ψᵢ and fillings nᵢ. 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 ψᵢ at a critical Δc: for Δ<Δc sites with substantial ψᵢ's percolate across the lattice; for Δ>Δc 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.