We introduce a separability condition for the states of fermion lattice systems. It shares similar characterizations about the state correlation between a pair of disjoint subsystems with that for the tensor-product systems. We propose two seemingly natural non-separable degrees for the fermion lattice system based on our generalization of the entanglement of formation to an arbitrary, namely not necessarily independent pair of finite-dimensional subsystems imbedded in a composite system. We show the equivalence of their zero (non-zero) value and the separability (non-separability). A class of even mixed states with a fermionic correlation giving rise to the non-separability is studied. The usage of the same formula just as the entanglement of formation is inappropriate for the fermion system, since it does not detect the non-separability between the fermion pair of subsystems for those states.
The case of polaron and bipolaron formation due to electron-phonon coupling was studied on a lattice with soft non-linear intersite interactions. The ground state of a system that consists of one or two electrons coupled to a non-linear lattice was obtained numerically. The binding energy of the bipolaron was examined as a function of the degree of the non-linearity of the lattice. A model was investigated where the interatomic interactions in the lattice are described by a double-well potential. This type of non-linear interaction strongly influences the bipolaron formation and generally improves its stability and increases its binding energy by permitting a local structural change of the lattice.