Mixed valence of the integrable magnetic impurity in correlated-electron hosts

Abstract

In this paper we show that the Bethe ansatz integrable theories for a magnetic impurity embedded in the correlated electron host correspond to the impurity which carries both spin and charge internal degrees of freedom. Therefore the magnetic impurity necessarily reveals either nonmagnetic behavior, the Kondo-like magnetic regime, or the mixed valence regime, depending on the values of the external magnetic field and the applied voltage, which control the band filling and the magnetization of the correlated-electron host. It is shown that several previously published papers contain invalid statements that the integrability demands only the Kondo exchange coupling of the magnetic impurity to the correlated host together with the action of the ``fine-tuned'' scalar static potential at the impurity site. We prove that instead of that static potential the integrability implies the dynamic scalar interaction of the impurity in the charge sector, too, which causes the valence of the impurity to depend on the external parameters and the parameters of the impurity-host coupling. We show how in the Bethe ansatz framework the effects of the dynamic impurity, external boundary potentials, applied to the edges of the open chain, and the effects of the free edges of the chain themselves are clearly separated. The impurity valence, magnetization, susceptibility, and the mesoscopic effects are calculated as functions of the impurity-host coupling, spin of the impurity, external magnetic field, applied voltage, and temperature for several one-dimensional exactly solvable models of highly correlated electrons. Limitations of the Bethe ansatz approach are discussed.