Slave rotor approach to exciton condensation in a two-band system

We have studied exciton formation and condensation in an extended Falicov-Kimball model, going beyond the weak coupling approach, employing a semi-analytical technique: the slave-rotor mean-field theory (SRMF). In this essentially strong coupling theory, charge and spin (or orbital/pseudospin) degrees are treated as independent degrees of freedom, coupled by a local constraint. Using a two-site-extension of SRMF, we capture the effective many body scale beyond conventional mean-field theory. While the formation of excitons is favoured by the interband hybridization , it is strongly influenced by the on-site Coulomb interaction . Beyond a critical hybridization, there is condensation of excitons, leading to a transition from a metal to an excitonic insulator phase. Moreover, the behaviour of excitonic averages differs from the usual Hartree-Fock mean-field theory. Low- results show that excitonic order parameter (Δ) is continuous across the transition both for single as well as two-site approximation, changing to weakly first order one at intermediate for the later. The large- limit shows a continuous transition for two-site analysis but remains first order in the single-site approximation. The slave rotor theory gives a mixed state of excitons and metal in both the analyses. We have also checked the effect of intersite correlation and localized band hopping on the exciton condensation.