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

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 Vc ≈ (1.6 ± 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 Vc ≈ (5.0 ±0.5)t at U = 4t.