Influence of hybridization on the properties of the spinless Falicov-Kimball model

Without a hybridization between the localized f- and the conduction (c-) electron states the spinless Falicov-Kimball model (FKM) is exactly solvable in the limit of high spatial dimension, →d∞, as first shown by Brandt and Mielsch. Here I show that at least for sufficiently small c-f interaction this exact inhomogeneous ground state is also obtained in Hartree-Fock approximation. With hybridization the model is no longer exactly solvable, but the approximation yields that the inhomogeneous charge-density wave (CDW) ground state remains stable also for finite hybridization V smaller than a critical hybridization Vc, above which no inhomogeneous CDW solution but only a homogeneous solution is obtained. The spinless FKM does not allow for a ``ferroelectric'' ground state with a spontaneous polarization, i.e., there is no nonvanishing 〈c^f〉 expectation value in the limit of vanishing hybridization.