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The Bose glass (BG) phase is the Griffiths region of the disordered BoseHubbard model (BHM), characterized by finite, quasi-superfluid clusters withina Mott insulating background. We propose to utilize this characterization toidentify the complete zero-temperature phase diagram of the disordered BHM in$d\ge2$ dimensions by analyzing the geometric properties of what we callsuperfluid (SF) clusters, which are defined to be clusters of sites withnon-integer expectation values for the local boson occupation number. The Mottinsulator (MI) phase then is the region in the phase diagram where no SFclusters exist, and the SF phase the region, where SF clusters percolate - theBG phase is in between: SF clusters exist, but do not percolate. Thisdefinition is particularly useful in the context of local mean field (LMF, orGutzwiller-Ansatz) calculations, where we show that an identification of thephases on the basis of global quantities like the averaged SF order parameterand the compressibility are misleading. We apply the SF cluster analysis to theLMF ground states of the two dimensional disordered BHM to produce its phasediagram and find a) an excellent agreement with the phase diagram predicted onthe basis of quantum Monte Carlo simulations for the commensurate density$n=1$, and b) large differences to stochastic mean field and other mean fieldpredictions for fixed disorder strength. The relation of the percolationtransition of the SF clusters with the onset of non-vanishing SF stiffnessindicating the BG to SF transition is discussed.

Superfluid clusters, percolation and phase transitions in the disordered, two dimensional Bose-Hubbard model