Abstract
We study the electron-hole pair (or excitonic) condensation in the extended Falicov-Kimball model at finite temperatures based on the cluster mean-field-theory approach, where we make the grand canonical exact-diagonalization analysis of small clusters using the sine-square deformation function. We thus calculate the ground-state and finite-temperature phase diagrams of the model, as well as its optical conductivity and single-particle spectra, thereby clarifying how the preformed pair states appear in the strong-coupling regime of excitonic insulators. We compare our results with experiment on Ta$_2$NiSe$_5$.
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