Quantum lattice fluctuations in the molecular-crystal model

Abstract

An analytical approach, based on the unitary transformation method, has been developed to study the effects of quantum lattice fluctuations on the Peierls transition in the one-dimensional half-filled spin- 1 2 Holstein model. The nonadiabatic effects due to finite phonon frequency ω 0>0 are treated through an energy-dependent electron–phonon scattering function δ( k′, k) and the Green's function method is used to implement the perturbation treatment. The dimerization gap and the phonon-staggered ordering parameter are obtained. We show that at a finite electron–phonon coupling constant, there exists always the Peierls dimerization for any finite phonon frequency in spin- 1 2 Holstein model. With increasing lattice fluctuations, the gap and the phonon-staggered ordering decrease gradually. Our results agree well with those of quantum Monte Carlo simulations.