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-->infinity, 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 salvable, 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 V-c, 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(dagger)f > expectation value in the limit of vanishing hybridization, [S0163-1829(99)03404-9].