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 ωp > 0 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 ωp increases the lattice distortion and the gap in the fermionic spectrum decreases gradually; at some critical value g2c or (ωp)c, 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.
Scopus Subject Areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- 71.30.+h metal-insulator transitions and other electronic transitions
- 71.38.-k polarons and electron-phonon interactions
- 71.45.Lr charge-density-wave systems