Local symmetry and impossibility of mixed valence in the Falicov-Kimball model

Abstract

It is pointed out that homogeneously mixed-valent and excitonic insulator phases proposed earlier for the Falicov-Kimball model break a local symmetry of the Hamiltonian. An Elitzur-type proof on the impossibility of spontaneously breaking a local symmetry is given to show that such phases are not possible at nonzero temperature. At zero temperature, the possibility of breaking a local symmetry is demonstrated in a related model, but it is argued that such symmetry breaking does not occur in the Falicov-Kimball model.