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.

14 pages (latex) and 3 postscipt figures