Toulouse points and non-Fermi-liquid states in the mixed-valence regime of the generalized Anderson model

We study the mixed-valence regime of a generalized Anderson impurity model using the bosonization approach. This single-impurity problem is defined by the U=infinity, Anderson model with an additional density-density interaction, as well as an explicit exchange interaction, between the impurity and conduction electrons. We find three points in the interaction parameter space at which all the correlation functions can be calculated explicitly. These points represent the mixed-valence counterparts of the usual Toulouse point for the Kondo problem, and are appropriately named the Toulouse points of the mixed-valence problem. Two of these Toulouse points exhibit a strong coupling, Fermi liquid behavior. The third one shows spin-charge separation; here, the spin-spin correlation functions are Fermi-liquid-like, the charge-charge correlation functions and the single-particle Green function have non-Fermi-liquid behaviors, and a pairing correlation function is enhanced compared to the Fermi liquid case. This third Toulouse point describes the intermediate mixed-valence phase we have previously identified. In deriving these results, we emphasize the importance of keeping track of the anticommutation relation between the fermion fields when applying the bosonization method to the mixed-valence problem.