One-Dimensional Kondo Lattice at Half Filling: Charge Properties
  The model of Kondo chain with $M$-fold degenerate band of conduction electrons of spin 1/2 at half filling interacting with localized spins $S$ is studied. It is shown that due to the instanton effects the spin sector reveals itself in optical conductivity. Namely, the density of the charge current at large wave vector $k \approx \pi$ is proportional to the density of topological charge of the staggered magnetization. As a consequence, the optical conductivity at $k = \pi$ would either have a gap equal to three spin gaps (for $|M - 2S| = $(even) when the spin spectrum is gapful), or show a psedogap $\sigma(\omega, k = \pi) \sim \omega^2$ for $|M - 2S|$ = (odd). 
A. M. Tsvelik (University of Oxford)