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

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 $κ\propto |μ- μ_c|^{-0.58\pm0.08}$ where $μ_c$ is the critical chemical potential. In the insulating phase, the localization length follows $ξ_l \propto |μ- μ_c|^{-ν_l}$ with $ν_l = 0.26 \pm 0.05$. Under the assumption of hyperscaling, the compressibility data leads to a correlation length exponent $ν_κ= 0.21 \pm 0.04$. Our results show that the exponents $ν_κ$ and $ν_l$ agree within statistical uncertainty. This confirms the assumption of hyperscaling with correlation length exponent $ν= 1/4$ 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 $ν= 1/2$ and $z = 2$.