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

The disordered Bose-Hubbard model in two dimensions at noninteger filling admits a superfluid to Bose-glass transition at weak disorder. Less understood are the properties of this system at strong disorder and energy densities corresponding to excited states. In this work, we study the Bose-glass transition of the ground state and the related finite energy localization transition, the mobility edge of the quasiparticle spectrum, a critical energy separating extended from localized quasiparticle excitations. To study these the fluctuation operator expansion is used. The level spacing statistics of the quasiparticle excitations, the fractal dimension and decay of the corresponding wave functions are consistent with a many-body mobility edge. 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 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.

Automated summary

This work investigates the properties of the disordered Bose-Hubbard model in two dimensions at different disorder strengths, including the superfluid to Bose-glass transition, the mobility edge of the quasiparticle spectrum, and finite energy localization transitions. The study shows that the level spacing statistics and wave function features of quasiparticle excitations are consistent with a many-body mobility edge.