We have developed a variational approach to treat the nonadiabaticity, that is, the quantum-lattice fluctuations, of the electron-phonon interactions in the one-dimensional half-filled spinless Anderson lattice model including Coulomb interaction between both types of electrons. The nonadiabaticity due to finite phonon frequency is treated through a variational polaronic-type wave function, in which two variational parameters δ and ${\mathrm{\tau }}^2$ are used to take into account the dynamical distortion and the squeezing effect of phonon modes. We have found that the quantum-lattice fluctuations gradually smoothes the valence transitions when the polaronic level ${\mathrm{\varepsilon }}_{\mathit{f}}$-v changes. We have shown that conditions somewhat different from those of Hewson and Newns should be satisfied for the occurrence of a significant reduction of the effective hybridization. The effect of the Coulomb repulsion U is to suppress the quantum-lattice fluctuations, that is, to suppress the reduction of the fluctuating-valence frequency and the relaxation shift. We have also discussed the valence-density-wave ordering in the symmetric case. Our results show that the quantum-lattice fluctuations disfavor the ordering and the lattice dimerization parameter decreases with increasing phonon frequency. We have pointed out the possibility of an order-disorder transition in such systems.

• Received 7 June 1993

DOI:https://doi.org/10.1103/PhysRevB.49.9539