A low temperature derivation of spin-spin exchange in Kondo lattice model

TL;DR

This paper presents a novel low-temperature derivation of spin-spin interactions in the Kondo lattice model using Hubbard-Stratonovich transformation and drone-fermion representations, revealing different regimes of magnetic coupling.

Contribution

It introduces a first-time drone-fermion representation for spin-3/2 and develops a path-integral formulation applicable to both weak and strong coupling regimes.

Findings

Reproduces RKKY interaction at weak coupling

Derives an effective local spin-spin interaction at strong coupling

Provides a unified low-temperature framework for the Kondo lattice model

Abstract

Using Hubbard-Stratonovich transformation and drone-fermion representations for spin-1/2 and for spin-3/2, which is presented for the first time, we make a path-integral formulation of the Kondo lattice model. In the case of weak coupling and low temperature, the functional integral over conduction fermions can be approximated to the quadratic order and this gives the well-known RKKY interaction. In the case of strong coupling, the same quadratic approximation leads to an effective local spin-spin interaction linear in hopping energy $t$