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

Abstract

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. is approached from the insulating phase. ξ l may be interpreted as the localization length involved in transferring a particle over a distance r from the electronic system to the heat bath lying at energy µ within the charge gap. Under the assumption of hyperscaling, the above quantities are expected to satisfy the scaling relations:where The Hubbard model we consider reads:Here, i, j denotes nearest-neighbors. c † i,σ (c i,σ ) creates (annihilates) an electron with zcomponent of spin σ on site i and n i,σ = c † i,σ c iσ . In this notation half-band filling corresponds to µ = 0. We start by considering the non-interacting case, U/t = 0. In Fourier space, the single particle energies are given by ǫ k = −2t(cos( k a x ) + cos( k a y )), a x , a y being the lattice constants. In this letter, the length scale is set by: | a x | = | a y | = 1. At zero temperature, an insulator-metal transition will occur when µ → µ c = 4t. For those chemical potentials, the zero-temperature Green function [3] at ω = µ is given by:where N denotes the number of sites of the square lattice and the factor 2 corresponds to the summation over the spin degrees of freedom. Numerically, one obtains: G( r, ω = µ) ∼ e Here, b † creates an electron in the impurity state at the origin and energy ǫ b . The hybridization between the localized state and the band electrons alters the energy of the impurity level to the value:. We will assume E b > ǫ k for all k. When all single

Quantum Mott Transition and Multi-Furcating Criticality

“…This large dynamical exponent z = 4 is indeed supported in a number of independent numerical calculations for the filling-control transition of the Hubbard model in two dimensions at T = 0, 23,24,36,[38][39][40][41] which suggests that T ch is zero or very small in this case.…”

Drude Weight of the Two-Dimensional Hubbard Model –Reexamination of Finite-Size Effect in Exact Diagonalization Study–

“…The diverging behavior of was reported by the quantum Monte Carlo (QMC) simulations 7,14) performed on the same model with larger system sizes not yet treated by exact-diagonalization studies. The QMC calculation 15) also demonstrated that the localization length suggests the divergence l / j À c j À with ¼ 1=4 as the chemical potential approaches the charge gap c from the insulating side. The scaling theory indicates z ¼ 1, which also leads to the exponent z ¼ 4.…”

Thermodynamic Relations in Correlated Systems

“…(18). For the two-dimensional system, d = 2, the dynamical exponent z = 4 was identified by numerical calculations, 23,24 and then the same critical behavior for χ c as the d = 1 case appears. For the three-dimensional system, in the case of z = 4, the charge compressibility has the form of χ c ∼ (µ c − µ) −1/4 by eq.…”