Coherent cellular dynamical mean-field theory: a real-space quantum embedding approach to disorder in strongly correlated electron systems

We formulate a quantum embedding algorithm in real-space for the simultaneous theoretical treatment of nonlocal electronic correlations and disorder, the coherent cellular dynamical mean-field theory (C-CDMFT). This algorithm combines the molecular coherent potential approximation with the cellular dynamical mean-field theory. After a pedagogical review of quantum embedding theories for disordered and interacting electron systems, and a detailed discussion of its work flow, we present first results from C-CDMFT for the half-filled two-dimensional Anderson-Hubbard model on a square lattice: (i) the analysis of its Mott metal-insulator transition as a function of disorder strength, and (ii) the impact of different types of disorder on its magnetic phase diagram. For the latter, by means of a ``disorder diagnostics'', we are able to precisely identify the contributions of different disorder configurations to the system's magnetic response.