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Slave rotor mean field (SRMF) theory is employed to study exciton formationin the extended Falicov-Kimball Model (EFKM). In this theory, charge and spin(or orbital) degrees are treated as independent degrees of freedom, coupled bya constraint. Using this formalism in single as well as cluster extension, wecapture the effective many body scales beyond conventional mean-field theory.While the formation of exciton is favored by the interband hybridization $V$,it is strongly influenced by the on-site Coulomb interaction $U$. Beyond acritical hybridization, there is a condensation of exciton, effectively givingrise to a crossover from metal to an excitonic insulator phase. The system goesfrom a metal to an excitonic insulating state, with a first order jump in theexcitonic order parameter. Moreover, the behavior of excitonic averages differsfrom earlier results from Hartree-Fock mean-field theory. Low-$U$ results showthat excitonic order parameter ($\Delta$) is continuous across the transitionboth for single as well as two-site approximation. The transition changes toweakly first order in the intermediate $U$ for cluster case. On the other hand,large $U$ limit shows a continuous transition for cluster but remains firstorder in the single-site approximation. The slave rotor also indicates anexcitonic metallic region in both single and cluster cases, while there is anorbital liquid in the insulating regime in the cluster theory. The $\Delta-V$graph shows step-like behavior when both the bands have the same parity. Forcluster approximation, a second order to first order transition in $\Delta-V$is obtained by tuning the hopping parameter of the localized band.

Slave Rotor Approach to Exciton Condensation in a Two-band System