Eur. Phys. J. B 25, 299-306 (2002)
https://doi.org/10.1140/epjb/e20020034

Effect of lattice fluctuations on the quantum phase transition in a one-dimensional commensurate system

¹ Department of Applied Physics, Shanghai Jiao Tong University, Shanghai 200030, PR China
² Department of Physics, Hong Kong Baptist University, Hong Kong, PR China
³ Department of Physics, Tamkang University, Tamsui, Taiwan 25137, PR China

Corresponding author: ^a hzheng@mail.sjtu.edu.cn

Received: 14 June 2001
Revised: 9 November 2001
Published online: 15 February 2002

Abstract

The effect of quantum lattice fluctuations on the properties of quantum phase transition in a one-dimensional commensurate system near and at criticality is studied. The nonadiabatic effect due to finite phonon frequency are treated through an energy-dependent electron-phonon scattering function introduced in a unitary transformation. By using the Green's function perturbation theory we have shown that our theory gives a good description of the effect of quantum lattice fluctuations: (1) At the criticality, when the coupling constant g² decreases or the phonon frequency increases the lattice distortion and the gap in the fermionic spectrum decreases gradually; at some critical value or (, the system becomes gapless and the lattice distortion disappears. (2) The calculated density of states do not have the inverse-square-root singularity but have a peak with a significant tail below the peak. (3) At the criticality our approach successfully describes the classical-quantum crossover. In the classical region the adiabatic mean-field parameters may strongly be renormalized by nonadiabatic corrections, and in the quantum region the phase transition is of the signature of a Kosterlitz-Thouless transition. (4) Away from the criticality the critical exponents for the energy gap and the ordering parameter have been calculated.