First - and Second Order Phase Transitions in the Holstein - Hubbard Model

– We investigate metal-insulator transitions in the half-filled Holstein-Hubbard model as a function of the on-site electron-electron interaction U and the electron-phonon coupling g. We use several different numerical methods to calculate the phase diagram, the results of which are in excellent agreement. When the electron-electron interaction U is dominant the transition is to a Mott-insulator; when the electron-phonon interaction dominates, the transition is to a localised bipolaronic state. In the former case, the transition is always found to be second order. This is in contrast to the transition to the bipolaronic state, which is clearly first order for larger values of U . We also present results for the quasiparticle weight and the double-occupancy as function of U and g. Strong correlation effects and localization can occur in metallic systems due both to strong electron-electron interactions and strong electron-phonon coupling and also their interplay. There are many systems with strongly correlated electrons where there is also a strong coupling to the lattice and lattice modes, for example V2O3 [1, 2], manganites [3] or fullerides [4]. The strong electron-electron interactions can be described by the Hubbard model, where the transition to a Mott-Hubbard insulator has been extensively investigated [5–9]. The Holstein model has been used to examine localization to a polaronic or bipolaronic insulator due to electron-phonon interactions [10–13]. The interplay between these two types of localization can be investigated using the Holstein-Hubbard model which includes both types of interaction: H = ∑ ~kσ ǫ(~k)c ~kσ c~kσ + U ∑