VALIDITY RANGES OF THE ADIABATIC AND ANTI-ADIABATIC APPROXIMATIONS INA 3-SITE CLUSTER MODEL

We analyse the validity ranges of the adiabatic and anti-adiabatic app roximations for a model with electron-electron and electron-phonon int eractions for a three-site cluster. This model describes the motion of apical oxygen atoms in YBa2Cu3O7. We show that the adiabatic approxim ation still applies for critical infrared coupling where the gap betwe en the ground state and first excited electronic state becomes nearly equal to the double-well potential barrier. For this high coupling val ue, the motion of holes and ions is already highly correlated. We arri ve at the non trivial conclusion that in this model the adiabatic appr oximation is valid even in a parameter region where the electronic ene rgy scale is not much larger than the phononic energy scale. This appr oximation is able to describe polaronic effects which have been shown to appear in the infrared absorption spectrum in previous exact numeri cal calculations. We also investigate the range of validity of the ant i-adiabatic approximation. We find that the window where none of the a bove-mentioned approximations is valid shrinks with decreasing on-site repulsion U until it closes at U = 0 in agreement with other work in the literature.