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We analyze the stability of excitonic ground states in the two-band Hubbardmodel with additional electron-phonon and Hund's rule couplings using acombination of mean-field and variational cluster approaches. We show that boththe interband Coulomb interaction and the electron-phonon interaction willcooperatively stabilize a charge density wave (CDW) state which typifies an"excitonic" CDW if predominantly triggered by the effective interorbitalelectron-hole attraction or a "phononic" CDW if mostly caused by the couplingto the lattice degrees of freedom. By contrast, the Hund's rule couplingpromotes an excitonic spin density wave. We determine the transition betweenexcitonic charge and spin density waves and comment on a fixation of the phaseof the excitonic order parameter that would prevent the formation of asuperfluid condensate of excitons. The implications for exciton condensation inseveral material classes with strongly correlated electrons are discussed.

Competition between excitonic charge and spin density waves: Influence of electron-phonon and Hund's rule couplings