QUANTUM MONTE-CARLO STUDY OF THE ONE-DIMENSIONAL HOLSTEIN MODEL OF SPINLESS FERMIONS

The Holstein model of spinless fermions interacting with dispersionles s phonons in one dimension is studied by a Green's function Monte Carl o technique. The ground-state energy, first fermionic excited state, d ensity wave correlations, and mean lattice displacements are calculate d 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 ho pping parameter of t=0.1 omega, omega, and 10 omega, where omega is th e phonon frequency. At a finite fermion-phonon coupling g there is a t ransition 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 t he Luttinger liquid parameters, u(rho), and K-rho, the velocity of cha rge excitations, and the correlation exponent respectively. For free f ermions (g=0) and for strong coupling (g(2) much greater than t omega) our results agree well with known analytic results.