Title: Formation and condensation of excitonic bound states in the generalized Falicov-Kimball model,
Abstract: The density-matrix-renormalization-group (DMRG) method and the Hartree-Fock
(HF) approximation with the charge-density-wave (CDW) instability are used to
study a formation and condensation of excitonic bound states in the generalized
Falicov-Kimball model. In particular, we examine effects of various factors,
like the $f$-electron hopping, the local and nonlocal hybridization, as well as
the increasing dimension of the system on the excitonic momentum distribution
$N(q)$ and especially on the number of zero momentum excitons $N_0=N(q=0)$ in
the condensate. It is found that the negative values of the $f$-electron
hopping integrals $t_f$ support the formation of zero-momentum condensate,
while the positive values of $t_f$ have the fully opposite effect. The opposite
effects on the formation of condensate exhibit also the local and nonlocal
hybridization. The first one strongly supports the formation of condensate,
while the second one destroys it completely. Moreover, it was shown that the
zero-momentum condensate remains robust with increasing dimension of the
system.