By employing the time-dependent exact diagonalization method, we investigate the photoexcited states of the excitonic insulator in the extended Falicov-Kimball model (EFKM). We here show that the pulse irradiation can induce the interband electron-electron pair correlation in the photoexcited states, while the excitonic electron-hole pair correlation in the initial ground state is strongly suppressed. We also show that the photoexcited states contains the eigenstates of the EFKM with a finite number of interband electron-electron pairs, which are responsible for the enhancement of the electron-electron pair correlation. The mechanism found here is due to the presence of the internal SU(2) pairing structure in the EFKM and thus it is essentially the same as that for the photoinduced η-pairing in the repulsive Hubbard model reported recently [T. Kaneko et al., Phys. Rev. Lett. 122, 077002 (2019)]. This also explains why the nonlinear optical response is effective to induce the electron-electron pairs in the photoexcited states of the EFKM. Furthermore, we show that, unlike the η-pairing in the Hubbard model, the internal SU(2) structure is preserved even for a nonbipartite lattice when the EFKM has the direct-type band structure, in which the pulse irradiation can induce the electron-electron pair correlation with momentum q = 0 in the photoexcited states. We also discuss briefly the effect of a perturbation that breaks the internal SU(2) structure.

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We develop the variational-cluster-approximation method based on the thermal-pure-quantumstate approach and apply the method to the calculations of the thermodynamic properties of the Hubbard model, thereby obtaining the temperature dependence of the single-particle excitation spectra, entropy and specific heat, and order parameter of the antiferromagnetic phase efficiently. We thus demonstrate that the method developed here has a potential power for elucidating finitetemperature properties of strongly correlated electron systems.

Using the variational cluster approach based on the self-energy functional theory, we study the possible occurrence of excitonic order and superconductivity in the two-orbital Hubbard model with intra-and inter-orbital Coulomb interactions. It is known that an antiferromagnetic Mott insulator state appears in the regime of strong intra-orbital interaction, a band insulator state appears in the regime of strong interorbital interaction, and an excitonic insulator state appears between them. In addition to these states, we find that the s ± -wave superconducting state appears in the small-correlation regime, and the d x 2 −y 2wave superconducting state appears on the boundary of the antiferromagnetic Mott insulator state. We calculate the single-particle spectral function of the model and compare the band gap formation due to the superconducting and excitonic orders.

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