Phase Diagram and Spectral Function of the Two-Dimensional Disordered Bose-Hubbard Model: A Real-Space Dynamical Mean-Field Theory Analysis

Abstract: We numerically investigate the two-dimensional Bose-Hubbard model with local onsite disorder, where the competition between disorder and short-range interactions leads to the emergence of a Bose glass (BG) phase between the Mott insulator (MI) and superfluid (SF) phases. In order to analyze the inhomogeneous system we employ real-space bosonic dynamical mean-field theory and perform an ensemble average over disorder realizations. To distinguish the MI from the BG phase, we compare the Edwards-Anderson order parameter and the compressibility with the energy gap condition. To identify the insulator to SF transition, we apply a percolation analysis to the condensate order parameter. In qualitative accordance with the theorem of inclusions we always find an intermediate BG phase between the SF and MI. However, the quantitative comparison indicates significant deviations between the MI to BG phase boundary expected in the thermodynamic limit and the one obtained for a finite system size. Analyzing the spectral function in the strong-coupling regime reveals evidence for analytically predicted damped localized modes in the dispersion relation.