Hidden integrability of a Kondo impurity in an unconventional host

We study a spin- {1}/{2} Kondo impurity coupled to an unconventional host in which the density of band states vanishes either precisely at (“gapless” systems) or on some interval around the Fermi level (“gapped” systems). Despite an essentially nonlinear band dispersion, the system is proven to exhibit hidden integrability and is diagonalized exactly by the Bethe ansatz. In addition, we show how a potential (spin independent) scattering at the impurity site is incorporated in the approach developed.