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

TL;DR

This paper develops a formalism for the Kondo lattice model using unitary transformations, revealing complex spin and charge excitations, and identifying a vacuum instability indicating a phase transition.

Contribution

It introduces a novel approach to express the Kondo lattice Hamiltonian with fermionic operators that approximate the ground state and excitations, uncovering strongly correlated charged modes and vacuum instability.

Findings

Identification of soft neutral modes with large low-temperature responses

Discovery of strongly correlated charged modes affecting the low-energy spectrum

Evidence of vacuum instability leading to a phase transition

Abstract

Using unitary transformations, we express the Kondo lattice Hamiltonian in terms of fermionic operators that annihilate the ground state of the interacting system and that represent the best possible approximations to the actual charged excitations. In this way, we obtain an effective Hamiltonian which, for small couplings, consists in a kinetic term for conduction electrons and holes, an RKKY-like term, and a renormalized Kondo interaction. The physical picture of the system implied by this formalism is that of a vacuum state consisting in 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, which lead to very large low-temperature values of the heat capacity and magnetic susceptibility, and charged modes corresponding to the excitation of electrons and holes in the system. Using the translational and spin rotational symmetries, we construct a simple ansatz to determine the charged excitations neglecting the effects of the spin correlations. Apart from the `normal', uncorrelated states, we find strongly correlated charged 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.