Constrained-path quantum Monte Carlo simulations of the zero-temperature disordered two-dimensional Hubbard model

Abstract

We study the effects of disorder on long-range antiferromagnetic correlations in the half-filled, two-dimensional, repulsive Hubbard model at $T=0.$ A mean field approach is first employed to gain a qualitative picture of the physics and to guide our choice for a trial wave function in a constrained path quantum Monte Carlo (CPQMC) method that allows for a more accurate treatment of correlations. Within the mean field calculation, we observe both Anderson and Mott insulating antiferromagnetic phases. There are transitions to a paramagnet only for relatively weak coupling, $U<2t$ in the case of bond disorder, and $U<4t$ in the case of on-site disorder. Using ground-state CPQMC we demonstrate that this mean field approach significantly overestimates magnetic order. For $U=4t,$ we find a critical bond disorder of ${V}_{c}\ensuremath{\approx}(1.6\ifmmode\pm\else\textpm\fi{}0.4)t$ even though within mean field theory no paramagnetic phase is found for this value of the interaction. In the site disordered case, we find a critical disorder of ${V}_{c}\ensuremath{\approx}(5.0\ifmmode\pm\else\textpm\fi{}0.5)t$ at $U=4t.$