Using linear response theory with the dynamical mean-field approximation we investigate the particle-hole instabilities of the two-band Hubbard model in the vicinity of the spin-state transition. Besides the previously reported high-spin--low-spin or
der we find an instability towards triplet excitonic condensate. We discuss the strong and weak coupling limits of the model, in particular, a connection to the spinful hard-core bosons with a nearest-neighbor interaction. Possible realization in LaCoO3 at intermediate temperatures is briefly discussed.
The low-temperature behavior of the asymmetric single-impurity Anderson model is studied by diagrammatic methods resulting in analytically controllable approximations. We first discuss the ways one can simplify parquet equations in critical regions
of singularities in the two-particle vertex. The scale vanishing at the critical point defines the Kondo temperature at which the electron-hole correlation function saturates. We show that the Kondo temperature exists at any filling of the impurity level. A quasiparticle resonance peak in the spectral function, however, forms only in almost electron-hole symmetric situations. We relate the Kondo temperature with the width of the resonance peak. Finally we discuss the existence of satellite Hubbard bands in the spectral function.
