Exactly solvable model of a one-dimensional Kondo lattice

Abstract

A one-dimensional model of the Kondo lattice for $\ensuremath{\nu}$ degenerate conduction electrons interacting with local moments arranged regularly is formulated. The model is integrable and reduces to the $\mathrm{SU}(\ensuremath{\nu}+1)$-invariant $t\ensuremath{-}J$ model with field splitting. We present the exact solution via Bethe's ansatz; the ground-state energy, the chemical potential, the Fermi momentum, and the Fermi velocity have been calculated numerically for an arbitrary density of the electrons. We observe that the electron velocity decays to zero in a small vicinity of the critical concentration of the conduction electrons, which is direct evidence of the metal--Kondo-insulator transition due to strong correlations.