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

Abstract

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 displacement 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 $t=0.1\omega$, $\omega$, and $10\omega$ where $\omega$ 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, $u_{\rho }$ and $K_{\rho }$, the velocity of charge excitations and the correlation exponent, respectively. For free fermions ($g=0$) and for strong coupling ($g^2\gg t\omega$) our results agree well with known analytic results. For $t=\omega$ and $t=10\omega$ our results are inconsistent with the metal-insulator transition being a Kosterlitz-Thouless transition.\\

16 pages of ReVTeX, 11 figures in uuencoded compressed tar file. Minor changes to text. Our results are inconsistent with the metal-insulator transition studied being a Kosterlitz-Thouless transition. The figures are now in the correct order. To appear in Physical Review B, April 15, 1996

References in corpus (2)

• One-Dimensional Fermi liquids
• Destruction of Peierls dimerization in the molecular crystal model: Effects of quantum phonon fluctuations

Cited by in corpus (42)

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