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We extend the self-energy functional theory (SFT) to the case of interactinglattice bosons in the presence of symmetry breaking and quenched disorder. Theself-energy functional we derive depends only on the self-energies of thedisorder-averaged propagators, allowing for the construction of generalnon-perturbative approximations. Using a simple single-site reference systemwith only three variational parameters, we are able to reproduce numericallyexact quantum Monte Carlo (QMC) results on local observables of theBose-Hubbard model with box disorder with high accuracy. At stronginteractions, the phase boundaries are reproduced qualitatively but shiftedwith respect to the ones observed with QMC due to the extremely low condensatefraction in the superfluid phase. Deep in the strongly-disorderedweakly-interacting regime, the simple reference system employed is insufficientand no stationary solutions can be found within its restricted variationalsubspace. By systematically analyzing thermodynamical observables and thespectral function, we find that the strongly-interacting Bose glass ischaracterized by different regimes, depending on which local occupations areactivated as a function of the disorder strength. We find that the particlesdelocalize into isolated superfluid lakes over a strongly localized backgroundaround maximally-occupied sites whenever these sites are particularly rare. Ourresults indicate that the transition from the Bose glass to the superfluidphase around unit filling at strong interactions is driven by the percolationof superfluid lakes which form around doubly occupied sites.

Self-energy functional theory with symmetry breaking for disordered lattice bosons