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

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

1995-10-16

arxiv.org/abs/cond-mat/9510084v1

Physics

Condensed Matter

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

Scientific paper

10.1103/PhysRevLett.76.3176

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 $z = 2$.

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