Scaling in an interacting two-component (valence-fluctuation) electron gas

A one-dimensional model of a two-component interacting electron gas with different Fermi wave vectors and Fermi velocities is considered. The method of the multiplicative renormalization group is used and the leading-order equations for the vertices as the frequency or momentum cutoff is reduced are derived. There are in general twelve different vertices in which there are logarithmic corrections in scaling, which may be broadly classified as intracomponent interactions, intercomponent exchange interactions, and charge-transfer interactions. The scaling equations are numerically solved in a limited regime appropriate for the valence-fluctuation problem. We discover that intercomponent charge-fluctuation interactions do not affect the dominant instabilities which are primarily determined by the intercomponent exchange interactions (provided intracomponent channels by themselves are stable, as in the range of parameters examined). The theoretical connection of the fluctuating-valence problem to the Kondo-like problems which is phenomenologically observed is thereby established.