Separability condition for the states of fermion lattice systems and its characterization

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 (nonseparability). 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. Mailing address: Institut des Hautes Études Scientifiques (IHÉS), Le Bois-Marie, 35, route de Chartres F-91440 Bures-sur-Yvette, FRANCE. e-mail:[email protected]