Exact numerical diagonalization of one-dimensional interacting electrons non-adiabatically coupled to phonons

We study the role of non-adiabatic Holstein electron-phonon coupling on the neutral-ionic phase transition of charge transfer crystals which can be tuned from continuous to discontinuous, using exact numerical diagonalization. The variation of electronic properties through the transition is smoothed by non-adiabaticity. Lattice properties are strongly affected, and we observe both squeezing and antisqueezing, depending on details of the adiabatic potentials, and identify the quantum uncertainty of the phonons as the most sensitive measure of non-adiabaticity. The adiabatic limit is regular for a continuous transition but turns out completely inadequate near a discontinuous transition. The relevance of coherent-state approaches is assessed critically.