Stable Quantum Monte Carlo Algorithm for T= 0 Calculation of Imaginary Time Green Functions

We present a numerically stable Quantum Monte Carlo algorithm to calculate zero-temperature imaginary-time Green functions G(r, τ) for Hubbard type models. We illustrate the efficiency of the algorithm by calculating the on-site Green function G(r = 0, τ) on 4 × 4 to 12 × 12 lattices for the two-dimensional half-filled repulsive Hubbard model at U/t = 4. By fitting the tail of G(r = 0, τ) at long imaginary time to the form e^-τΔε, we obtain a precise estimate of the charge gap: Δ_c = 0.67±0.02 in units of the hopping matrix element. We argue that the algorithm provides a powerful tool to study the metal-insulator transition from the insulator side.