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

We use quantum Monte Carlo methods to determine T0ex0ex=0ex0ex0 Green functions, G(→r,ω), on lattices up to 16×16 for the 2D Hubbard model at U/t0ex0ex=0ex0ex4. For chemical potentials μ within the Hubbard gap |μ|<μc and at long distances →r, $G({{→}}{r},{ω}{{0ex}{0ex}}={{0ex}{0ex}}{μ}){~}{e}^{{-}|{{→}}{r}|/{{ξ}}ₗ}$ with critical behavior ${{ξ}}ₗ{~}|{μ}{-}{{μ}}c{|}^{{-}{ν}}$, ${ν}{{0ex}{0ex}}={{0ex}{0ex}}0.26±{}0.05$. This result stands in agreement with the assumption of hyperscaling with correlation exponent ${ν}{{0ex}{0ex}}={{0ex}{0ex}}1/4$ and dynamical exponent $z{{0ex}{0ex}}={{0ex}{0ex}}4$. In contrast, the generic band insulator as well as the metal-insulator transition in the 1D Hubbard model are characterized by ${ν}{{0ex}{0ex}}={{0ex}{0ex}}1/2$ and $z{{0ex}{0ex}}={{0ex}{0ex}}2$.