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We study the weakly disordered Bose-Hubbard model on a cubic lattice througha one-loop renormalization group analysis of the corresponding effective fieldtheory which is explicitly derived by combining a strong-coupling expansionwith a replica average over the disorder. The method is applied not only togeneric uncorrelated on-site disorder but also to simultaneous hopping disordercorrelated with the differences of adjacent disorder potentials. Suchcorrelations are inherent in fine-grained optical speckle potentials used as asource of disorder in optical lattice experiments. As a result of strongcoupling, the strength of the replica mixing disorder vertex, responsible forthe emergence of a Bose glass, crucially depends on the chemical potential andthe Hubbard repulsion and vanishes to leading order in the disorder atcommensurate boson fillings. As a consequence, at such fillings a directtransition between the Mott-insulator and the superfluid in the presence ofdisorder cannot be excluded on the basis of a one-loop calculation. Atincommensurate fillings, at a certain length scale, the Mott insulator willeventually become unstable towards the formation of a Boss glass. Phasediagrams as a function of the microscopic parameters are presented and thefinite-size crossover between the Mott-insulating state and the Bose glass isanalyzed.

Anomalous suppression of the Bose glass at commensurate fillings in the disordered Bose-Hubbard model