Inhomogeneous mean-field approach for collective modes at the superfluid-Mott glass transition

We employ an inhomogeneous mean-field approach plus Gaussian fluctuations to investigate disordered Bose-Hubbard models with particle-hole symmetry in two and three dimensions. Within this framework, the collective excitations, i.e., Goldstone mode and the Higgs (amplitude) mode, are described by two effective, decoupled, disordered single-particle Hamiltonians whose properties are determined by the underlying mean-field solution. Based on multifractal analysis, we investigate the localization properties of each mode separately as a function of energy and the distance from the superfluid-Mott glass transition. Furthermore, we calculate susceptibility functions and compare the results with Monte Carlo simulations and experiments.