ABSTRACT
This chapter introduces the Hubbard model and the Holstein-Hubbard model and discusses the charge-density wave-spin density wave transition. The most suitable model to study the interplay between the electron-phonon interaction and the Coulomb repulsion in narrow-band systems is the Holstein-Hubbard model. Krishna, Mukhopadhyay, and Chatterjee have considered an extended Holstein-Hubbard model in one dimension so that the exact Bethe ansatz solution can be taken advantage of for the effective electronic problem and employed a better phonon variational state. The chapter also discusses the nature of the self-trapping (ST) transition, particularly whether the transition is continuous or discontinuous. In view of the potential role of small polarons in high Tc superconductors and colossal magneto-resistance materials, it is certainly more important to understand the nature of the ST transition in small polaron models. Das and Sil have studied the ST transition for a many-polaron system in the two-dimensional HH model.
