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.