Abstract
We study the Coulomb-interaction induced spontaneous symmetry breaking of the excitonic insulator state in the two-dimensional extended Falicov-Kimball model. Using the variational cluster approximation, we evaluate the order parameter, single-particle excitation gap, momentum distribution functions, and anomalous Green's function as a function of U at zero temperature. We find that in the weak-to-intermediate couplinb regime, the Fermi surface is well-defined and the calculated results can be understood in the close correspondence with the BCS theory, whereas in the strong-coupling regime, the Fermi surface is ill-defined and the results are consistent with the picture of BEC.
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