Phase transitions in a generalized Hubbard model

Introducing different bandwidths t(1) and t(2) in the Hubbard model, and allowing the spinless particles to transform from one band to another (hybridization) gives a generalized Hubbard model. The problem of electron phase transitions under pressure in mixed-valence materials is studied in the generalized model and is shown to be analogous to the problem of finding magnetization in the presence of an external field in the original Hubbard model. In the strong-interaction limit and exactly at half-filling, we find a strict correspondence between the excitonic state correlations in the mixed valence system and the quantum spin-liquid state. In addition, a first order phase transition from a quantum excitonic state to a valence density wave state under change of external field or temperature is also obtained. The magnetization and the phase diagram of the Hubbard model, for t(1) -> t(2), is also investigated, and the lability point for the transition from spin liquid state to ferromagnetic state is obtained.