Insulator-Metal Transition in the One and Two-Dimensional Hubbard Models

Abstract

We use Quantum Monte Carlo methods to determine $T=0$ Green functions, $G(\vec{r}, ω)$, on lattices up to $16 \times 16$ for the 2D Hubbard model at $U/t =4$. For chemical potentials, $μ$, within the Hubbard gap, $ |μ| < μ_c$, and at {\it long} distances, $\vec{r}$, $G(\vec{r}, ω= μ) \sim e^{ -|\vec{r}|/ξ_l}$ with critical behavior: $ξ_l \sim | μ- μ_c |^{-ν}$, $ ν= 0.26 \pm 0.05$. This result stands in agreement with the assumption of hyperscaling with correlation exponent $ν= 1/4$ and dynamical exponent $z = 4$. In contrast, the generic band insulator as well as the metal-insulator transition in the 1D Hubbard model are characterized by $ν= 1/2$ and $z = 2$.