Finite-size scaling analysis of localization transitions in the disordered two-dimensional Bose-Hubbard model within the fluctuation operator expansion method

Abstract

The disordered Bose-Hubbard model in two dimensions at non-integer filling admits a superfluid to Bose-glass transition at weak disorder. Far less understood are the properties of this system at strong disorder and energy density far from the ground state. In this work we put the Bose-glass transition of the ground state in relation to a finite energy localization transition, the mobility edge of its quasiparticle spectrum, which is a critical energy separating extended from localized excitations. We use the fluctuation operator expansion, which also considers effects of many-body entanglement. The level spacing statistics of the quasiparticle excitations, the fractal dimension and decay of the corresponding wavefunctions are consistent with a many-body mobility edge, while the finite-size scaling of the lowest gaps yields a correction to the mean-field prediction of the superfluid to Bose-glass transition. In its vicinity we further discuss spectral properties of the ground state in terms of the dynamic structure factor and the spectral function which also shows distinct behavior above and below the mobility edge.