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

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

1996-05-08

arxiv.org/abs/cond-mat/9605047v2

Physics

Condensed Matter

Two references added. The DVI file and PS figure files are also available at http://www.issp.u-tokyo.ac.jp/labs/riron/imada/fu

Scientific paper

10.1143/JPSJ.65.2339

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 $z = 2$.

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