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 $\kappa \propto |\mu -{\mu }_c{|}^{-0.58\pm 0.08}$ 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 $z=2$.

arXiv commentTwo references added. The DVI file and PS figure files are also available at http://www.issp.u-tokyo.ac.jp/labs/riron/imada/furukawa/; to appear in J. Phys. Soc. Jpn 65 (1996) No. 7

References in corpus (3)

• Insulator-Metal Transition in the One and Two-Dimensional Hubbard Models
• Stable Quantum Monte Carlo Algorithm for $T=0$ Calculation of Imaginary Time Green Functions
• Singularity of the density of states in the two-dimensional Hubbard model from finite size scaling of Yang-Lee zeros

Cited by in corpus (1)

• Quantum Transition between an Antiferromagnetic Mott Insulator and $d_{x^2-y^2}$ Superconductor in Two Dimensions