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

Abstract

We present a numerically stable Quantum Monte Carlo algorithm to calculate zero-temperature imaginary-time Green functions $ G(\vec{r}, \tau) $ for Hubbard type models. We illustrate the efficiency of the algorithm by calculating the on-site Green function $ G(\vec{r}=0, \tau) $ on $4 \times 4$ to $12 \times 12$ lattices for the two-dimensional half-filled repulsive Hubbard model at $U/t = 4$. By fitting the tail of $ G(\vec{r}=0, \tau) $ at long imaginary time to the form $e^{-\tau \Delta_c}$, we obtain a precise estimate of the charge gap: $\Delta_c = 0.67 \pm 0.02$ 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.