Kondo lattice model: Unitary transformations, spin dynamics, strongly correlated charged modes, and vacuum instability

Abstract

Using unitary transformations, we express the Kondo lattice Hamiltonian in terms of an optimal set of canonical operators obtaining an effective Hamiltonian which, for small couplings, consists of a kinetic term for electrons and holes, an RKKY term, and a renormalized Kondo interaction. The physical picture of the system implied by this formalism is that of a vacuum state consisting of a background of RKKY-induced spin correlations, where two kinds of elementary modes can be excited: soft neutral modes associated with deformations of the spin liquid, and charged modes corresponding to the excitation of electrons and holes. We study the charged modes, finding, apart from the ‘normal’, uncorrelated states, strongly correlated modes involving soft electrons (or holes) and spin fluctuations, which strongly renormalize the low-energy charged spectrum, and whose energy becomes negative beyond a critical coupling, signaling a vacuum instability and a transition to a new phase.