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

TL;DR

This study investigates the insulator-metal transition in 1D and 2D Hubbard models using Quantum Monte Carlo, revealing critical behavior and exponents that differ from band insulators and 1D cases.

Contribution

It provides detailed quantum Monte Carlo analysis of the 2D Hubbard model's insulator-metal transition, identifying unique critical exponents and scaling behavior.

Findings

Critical correlation length exponent ν ≈ 0.26

Agreement with hyperscaling assumptions (ν=1/4, z=4)

Different exponents from band insulators and 1D Hubbard model

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 $z = 2$.