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

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