Electron-phonon coupling in a one-band MX-chain model. A numerical study

We report and compare results on the ground state energy, renormalized phonon frequency, and optical conductivity of a one-band model for finite MX-chains at half-filling obtained within three types of methods: by exact Lanczos diagonalization, by factorizing the total wave function of the electron-phonon system (adiabatic ansatz), and within the analytical methods of the conventional many-body theory (mean-field, bubble approximation).