Interplay of Disorder and Correlation in Two-Dimensional Anderson–Hubbard Systems

Two-dimensional disordered correlated systems generally do not exhibit a true metal–insulator transition (MIT) for non-interacting electrons, according to the single-parameter scaling theory of Abrahams et al., which predicts that all states localize in 2D at zero temperature. However, the presence of strong electron–electron interactions may marginally alter this picture. In this work, to investigate the interplay of disorder and correlation beyond the non-interacting limit, we apply the typical medium dynamical cluster approximation (TMDCA) to the Anderson–Hubbard model on a 2D square lattice. The TMDCA, as a typical medium-based extension of dynamical cluster approximation, systematically captures spatial correlations necessary for disorder-induced coherent backscattering, while treating the Hubbard interaction at the second-order perturbation theory (SOPT) level. Our results provide a non-local perspective on how interactions may enable a crossover between metallic-like and localized regimes in two dimensions, offering new insight into the disorder–interaction phase diagram of 2D systems.