We analyze the stability of excitonic ground states in the two-band Hubbard model with additional electron-phonon and Hunds rule couplings using a combination of mean-field and variational cluster approaches. We show that both the interband Coulomb i
nteraction and the electron-phonon interaction will cooperatively stabilize a charge density wave (CDW) state which typifies an excitonic CDW if predominantly triggered by the effective interorbital electron-hole attraction or a phononic CDW if mostly caused by the coupling to the lattice degrees of freedom. By contrast, the Hunds rule coupling promotes an excitonic spin density wave. We determine the transition between excitonic charge and spin density waves and comment on a fixation of the phase of the excitonic order parameter that would prevent the formation of a superfluid condensate of excitons. The implications for exciton condensation in several material classes with strongly correlated electrons are discussed.
A comparative study is made on the metal-insulator transition of Dirac fermions in the honeycomb and pi-flux Hubbard models at half filling by means of the variational cluster approximation and cluster dynamical impurity approximation. Paying particu
lar attention to the choice of the geometry of solver clusters and the inclusion of particle-bath sites, we show that the direct transition from the Dirac semimetallic state to the antiferromagnetic Mott insulator state occurs in these models, and therefore, the spin liquid phase is absent in the intermediate region, in agreement with recent quantum-Monte-Carlo--based calculations.
Excitonic density-wave states realized by the quantum condensation of electron-hole pairs (or excitons) are studied in the two-band Hubbard model with Hunds rule coupling and the pair hopping term. Using the variational cluster approximation, we calc
ulate the grand potential of the system and demonstrate that Hunds rule coupling always stabilizes the excitonic spin-density-wave state and destabilizes the excitonic charge-density-wave state and that the pair hopping term enhances these effects. The characteristics of these excitonic density-wave states are discussed using the calculated single-particle spectral function, density of states, condensation amplitude, and pair coherence length. Implications of our results in the materials aspects are also discussed.
