Effect of quantum fluctuations on the Peierls dimerization in the one-dimensional molecular-crystal model

The effect of quantum lattice fluctuations on the Peierls dimerization is investigated in a half-filled one-dimensional molecular-crystal model. The nonadiabatic effects due to finite phonon frequency {ω} are treated through a variational polaron wave function: A part of the lattice distortion is carried over by the electrons and interferes with the static (frozen) lattice deformation. This leads to a weakening of the effective (adiabatic) potential stabilizing the dimerized state. Our results in the {ω}=0 (adiabatic) and {ω}={∞} (nonadiabatic) limits are in agreement with previous results. Moreover, in the finite-{ω} case we show that the lattice fluctuations are ``squeezed'' by the electron band motion, and the phonon subsystem is in the so-called two-phonon coherent state. The finite-{ω} results are in good agreement with both Monte Carlo simulations and renormalization-group analysis: For the spinless case an order-disorder transition is found on increasing the phonon frequency. On the contrary, the system for spin-1/2 electrons is always ordered, but the order parameter is slightly reduced when {ω} increases. The competition with singlet superconductive ordering is also examined. For {ω}={∞} the system is found to be on the borderline between charge-density wave (CDW) and superconducting, while for finite-{ω} CDW ordering prevails. Further extensions of this work are indicated.