Semiclassical solution of one dimensional model of Kondo insulator

The model of a Kondo chain with an M-fold degenerate band of conduction electrons of spin 1/2 at half filling interacting with localized spins S is studied. It is shown that in the continuous limit the spectrum of spin excitations is described by the O (3) nonlinear sigma model with the topological term with = (2S-M). Thus for -2S = (even) the system is an insulator and single electron excitations at low energies are massive spin polarons. Otherwise the density of states has a pseudogap and vanishes only at the Fermi level.