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

In this paper we show that the Bethe ansatz integrable theories for a magne tic impurity embedded in the correlated electron host correspond to the imp urity which carries both spin and change internal degrees of freedom. There fore 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 co ntrol the band filling and the magnetization of the correlated-electron hos t. It is shown that several previously published papers contain invalid sta tements that the integrability demands only the Kondo exchange coupling of the magnetic impurity to the correlated host together with the action of th e "fine-tuned'' scalar static potential at the impurity site. We prove that instead of that static potential the integrability implies the dynamic sca lar interaction of the impurity in the charge sector, too, which causes the valence of the impurity to depend on the external parameters and the param eters of the impurity-host coupling. We show how in the Bethe ansatz framew ork the effects of the dynamic impurity, external boundary potentials, appl ied to the edges of the open chain, and the effects of the free edges of th e chain themselves are clearly separated. The impurity valence, magnetizati on, susceptibility, and the mesoscopic effects are calculated as functions of the impurity-host coupling, spin of the impurity, external magnetic fiel d, applied voltage, and temperature for several one-dimensional exactly sol vable models of highly correlated electrons. Limitations of the Bethe ansat z approach are discussed. [S0163-1829(99)05046-8].