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

A model for correlated electrons in a lattice with local additional spin-1 degrees of freedom inducing constrained hopping is studied both in the low density limit and at quarter filling. We show that in both $1\mathrm{D}$ and $2\mathrm{D}$ two particles form a bound state even in the presence of a repulsive $U<\mathrm{}{U}_c$. A picture of a dilute Bose gas, leading to off-diagonal long-range order (LRO) in $2\mathrm{D}$ (quasi-LRO in $1\mathrm{D}$), is supported by quantitative calculations in 1D which allow for a determination of the phase diagram.