Insulator-metal transition in the one- and two-dimensional hubbard models

We use quantum Monte Carlo methods to determine T = 0 Green functions, G(r^→, ω) on lattices up to 16 × 16 for the 2D Hubbard model at U/T = 4. For chemical potentials μ within the Hubbard gap |μ| < μ_cand at long distances r^→, G(r^→ ω = μ) ∼e^{−|r→|/ξ_l} with critical behavior ξ_l ∼ |μ − μ_c|^−ν ν = 0.026 ±0.05 This result stands in agreement with the assumption of hyperscaling with correlation exponent ν = 1/4 and dynamical exponent z = 4. In contrast, the generic band insulator as well as the metal-insulator transition in the 1D Hubbard model are characterized by ν = 1/2 and z = 2.