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

Abstract

We use Quantum Monte Carlo methods to determine $T=0$ Green functions, $G(\vec{r},\omega )$, on lattices up to $16\times 16$ for the 2D Hubbard model at $U/t=4$. For chemical potentials, $\mu$, within the Hubbard gap, $|\mu |<{\mu }_c$, and at {\it long} distances, $\vec{r}$, $G(\vec{r},\omega =\mu )\sim e^{-|\vec{r}|/{\xi }_l}$ with critical behavior: ${\xi }_l\sim |\mu -{\mu }_c{|}^{-\nu }$, $\nu =0.26\pm 0.05$. This result stands in agreement with the assumption of hyperscaling with correlation exponent $\nu =1/4$ 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 $\nu =1/2$ and $z=2$.

9 pages (latex) and 5 postscript figures. Submitted for publication in Phys. Rev. Lett