Quantum Monte Carlo study of the one-dimensional Holstein model of spinless fermions

The Holstein model of spinless fermions interacting with dispersionless phonons in one dimension is studied by a Green's function Monte Carlo technique. The ground-state energy, first fermionic excited state, density wave correlations, and mean lattice displacements are calculated for lattices of up to 16 sites, for one fermion per two sites, i.e., a half-filled band. Results are obtained for values of the fermion hopping parameter of t=0.1{ω}, {ω}, and 10{ω}, where {ω} is the phonon frequency. At a finite fermion-phonon coupling g there is a transition from a metallic phase to an insulating phase in which there is charge-density-wave order. Finite-size scaling is found to hold in the metallic phase and is used to extract the coupling dependence of the Luttinger liquid parameters, u_ρ and K_ρ, the velocity of charge excitations, and the correlation exponent, respectively. For free fermions (g=0) and for strong coupling (g²{}t{ω}) our results agree well with known analytic results. {} 1996 The American Physical Society.