Understanding the Bose glass phase via a percolation scenario

We carry out a detailed investigation of the Bose glass (BG) phase that interrupts a direct transition from a superfluid to a Mott insulating phase in a two dimensional disordered Bose Hubbard Model. The accurate distinction between various phases is done via computing a number of relevant physical quantities such as a ratio of the sites containing integer density of the bosons to that of the total number of sites, compressibility, or a close variant of it, that is the relative fluctuation of the boson density and the entropy. Quite intriguingly, assuming the appearance of a spanning cluster of sites with integer occupancy to signal the onset of the BG phase, we find that the percolation threshold is same as that of random site percolation model in two dimensions. This similarity between two completely different systems is thought to be accidental, but may open up more studies in the future to critically examine the issue. Further, with the data obtained from our analysis, we have been able to obtain a complete phase diagram defined by the local interparticle interaction parameter (U) and the chemical potential (mu) averaged over several random configurations at different disorder values.