Phase transitions and percolating superfluid clusters in the disordered Bose-Hubbard model

The zero-temperature phase diagram of the disordered Bose-Hubbard model is critically re-examined on the basis of a local mean field (LMF) theory. It is demonstrated that in LMF theory the superfluid (SF) order parameter is non-zero even inside the Mott-lobes and the Bose-glass (BG) phase and therefore does not indicate a sharp BG to SF transition. This is also true for the compressibility, which indicates the MI to BG transition. This conflicts with other mean field approximations, which predict sharp transitions between MI-BG-SF. The origin of the non-vanishing SF order parameter within the putative BG phase is a finite density of disconnected SF islands in a sea of insulating sites, which are shown to percolate at the BG-SF transition. In accordance herewith the probability density function (PDF) of the local SF parameters has a non-vanishing mean and a delta-peak at zero SF parameter representing the insulating background. It is argued that in mean field theory only this characteristics of the PDF of local SF parameter and a percolation analysis of SF clusters is a reliable predictor for the phase boundaries. Phase transitions in the disordered Bose-Hubbard model 2