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While excitonic instabilities in multiorbital systems recently have comeunder scrutiny in a variety of transition-metal compounds, understandingemergence of these instabilities from strong electronic interactions hasremained a challenge. Here, we present a sign-problem-free determinant quantumMonte Carlo study of excitonic density orders in a half-filled two-orbitalHubbard-Kanamori model with broken orbital degeneracy, which accounts for therole of Hund's coupling in transition-metal compounds. For strong inverted(negative) Hund's exchange, we find numerical evidence for the emergence ofexcitonic density order, with competition between anti-ferro-orbital order and$\mathbf{Q} = (\pi,\pi)$ excitonic density order as a function of orbitalsplitting and Hund's coupling. While inverted Hund's coupling stabilizes aspin-singlet excitonic density phase for weak orbital splitting, positiveHund's coupling favors a spin-triplet excitonic density phase.

Sign-Free Determinant Quantum Monte Carlo Study of Excitonic Density Orders in a Two-Orbital Hubbard-Kanamori Model