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We investigate the half-filled two-orbital Hubbard model with the crystallineelectric field using dynamical mean-field theory combined with thecontinuous-time quantum Monte Carlo simulations. We systematically study howthe interplay of the intra- and interorbital Coulomb interations together withthe Hund coupling realizes the diagonal and off-diagonal ordered states. It isfound that the antiferroorbital ordered state is realized in the Hubbard model,in addition to the antiferromagnetically ordered and excitonic states. Thecompetition between the antiferroorbital ordered and excitonic states close tothe band insulating state is addressed.

Symmetry breaking states in the half-filled two-orbital Hubbard model with crystalline electric field