Critical Exponents of the Metal-Insulator Transition in the Two-Dimensional Hubbard Model

TL;DR

This study uses quantum Monte Carlo methods to analyze the critical behavior of the metal-insulator transition in the two-dimensional Hubbard model, confirming hyperscaling with specific critical exponents.

Contribution

It provides the first detailed determination of critical exponents for the filling-controlled transition in the 2D Hubbard model, supporting hyperscaling assumptions.

Findings

Compressibility diverges with exponent ~0.58 near criticality.

Localization length diverges with exponent ~0.26.

Critical exponents are consistent with hyperscaling and a correlation length exponent of 1/4.

Abstract

We study the filling-controlled metal-insulator transition in the two-dimensional Hubbard model near half-filling with the use of zero temperature quantum Monte Carlo methods. In the metallic phase, the compressibility behaves as $\kappa \propto |\mu - \mu_c|^{-0.58\pm0.08}$ where $\mu_c$ is the critical chemical potential. In the insulating phase, the localization length follows $\xi_l \propto |\mu - \mu_c|^{-\nu_l}$ with $\nu_l = 0.26 \pm 0.05$. Under the assumption of hyperscaling, the compressibility data leads to a correlation length exponent $\nu_\kappa = 0.21 \pm 0.04$. Our results show that the exponents $\nu_\kappa$ and $\nu_l$ agree within statistical uncertainty. This confirms the assumption of hyperscaling with correlation length exponent $\nu = 1/4$ and dynamical exponent $z = 4$. In contrast the metal-insulator transition in the generic band insulators in all dimensions as well as in the one-dimensional Hubbard model satisfy the hyperscaling assumption with exponents $\nu = 1/2$ and $z = 2$.