Phase Diagram of a Model of Correlated Hopping of Electrons in a Lattice of Berry Molecules

The $1D$ phase diagram of a model for correlated hopping of electrons in a lattice of Berry phase molecules is presented. Electrons hop in presence of an extra orbital degree of freedom at each site. This is mimicked as a spin-1 variable whose allowed states depend on the electron occupancy so as to take into account the orbital degeneracies of different molecular occupancies. In the $1D$ case we find that at low electron densities $nU_c$ and the system becomes an insulator. A spin-gap characterizes the phase-diagram for all densities and for all values of $U$, even in the metallic regime $U>U_c$.