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The electronic properties of excitonic insulators have been examinedprecisely in recent years. Pictures of exciton condensation may be applied tothe spin-state transition observed in perovskite cobalt oxides. We examine thecrystal-field and magnetic-field dependences of spatial spin structures on thebasis of the density matrix renormalization group method using an effectivemodel for the one-dimensional two-orbital Hubbard model in strong-couplinglimit. We find an excitonic insulating (EI) phase and a spin-state ordering(SSO) phase in the intermediate region between low-spin and high-spin phases.In the EI phase, spin-triplet excitons are spatially fluctuating due to quantumeffects, and an incommensurate spin correlation realizes. The analyses of aspin gap and degeneracy of entanglement spectra suggest the realization of theHaldane-like edge state in the EI phase. In the SSO phase, 3-fold orincommensurate SSO structures realize depending on the crystal-field splitting.These structures are stabilized as a result of the competition of exchangeinteractions between spin states.

Excitonic Correlations, Spin-State Ordering, and Magnetic-Field Effects in One-Dimensional Two-Orbital Hubbard Model for Spin-Crossover Region