Electron-phonon interaction for adiabatic anharmonic phonons

A model with Holstein-like electron-phonon coupling is studied in the limit of adiabatic phonons. The phonon distribution is anharmonic with two degenerate maxima. This model can be related to fermions in a correlated binary alloy and describes microscopic phase separation. We discuss the weak and strong electron-phonon coupling limits and present a qualitative phase diagram. In terms of the phononic displacements it consists of a homogeneous, an alternating, and a disordered phase. There is a first-order phase transition between the homogeneous and the alternating phases, and a second-order phase transition between the alternating and the disordered phases. The opening of a gap inside the disordered phase is treated using dynamical mean-field theory.