Effects of quantum phonon fluctuations in Peierls ground states

Recent research progress on the effects of quantum phonon fluctuations in t he Peierls ground state of one-dimensional electron-phonon interacting syst ems is presented. After a brief review on the related work, an equation for the dimerization order parameter within a one-loop approximation is derive d using a functional integral approach. For the one-dimensional molecular-c rystal Holstein model, it has been shown for the first time that Peierls di merization is destroyed by the quantum phonon fluctuations, so that there i s a transition from an insulating phase with charge-density-wave long-range order to a Luttinger liquid (metallic) phase. This result has been confirm ed very recently by other groups. For the Su-Schrieffer-Heeger model of con jugated polymers, it has been found that: (i) the frequency of the optical phonon at zero momentum vanishes in the system with weak electron-phonon co upling at Gross-Neveu limit; (ii) the fluctuations will be reduced in non-d egenerate conjugated polymers; () the interchain coupling between two neigh boring polymer chains suppresses partly the quantum fluctuations and then t he ground state is dimerized even for the spinless Fermion systems.