Phase diagram of the one-dimensional molecular-crystal model with Coulomb interactions: Half-filled-band sector

We discuss the ground-state phase diagram of the molecular-crystal model for electron-phonon interactions in the presence of on-site (U) and nearest-neighbor (V) electron-electron interactions in the half-filled-band sector. The system is analyzed as a function of the phonon frequency ({ω}), electron-phonon coupling constant ({λ}), and U and V in the physically relevant case (U,V>0). We discuss various limiting cases with perturbation theory, as well as intermediate-coupling cases using a numerical simulation technique. In particular, we study in detail the limit {ω}{→}{∞}, which corresponds to the extended Hubbard model. The phase diagram is divided into regions of long-range charge-density-wave (CDW) order, algebraic spin-density-wave (SDW) order, and coexisting algebraic singlet superconducting and CDW order. The transition between CDW and SDW phases is continuous for small U and first order for large U. For the physical parameter range (U,V>0), there is no regime where superconductivity dominates. Modification of this picture for the non-half-filled-band sector is indicated.