Effective action for the Kondo lattice model. New approach for S=1/2

TL;DR

This paper introduces a novel representation of spin operators in the Kondo lattice model, enabling a simplified diagrammatic technique and deriving an effective action for the nearly antiferromagnetic case.

Contribution

A new spin operator representation using Fermi operators with imaginary chemical potential, simplifying diagrammatic calculations in the Kondo lattice model.

Findings

New Green's functions with shifted Matsubara frequencies for S=1/2.

A straightforward temperature diagram technique without complex combinatorics.

Derivation of the effective action for the nearly antiferromagnetic Kondo lattice.

Abstract

In the partition function of the Kondo lattice, spin matrices are exactly replaced by bilinear combinations of Fermi operators with the purely imaginary chemical potential lambda=-i.pi.T/2 (Popov representation). This new representation of spin operators allows one to introduce new Green's functions with Matsubara frequencies 2.pi.T(n+1/4) for S=1/2. A simple temperature diagram technique is constructed with the path integral method. This technique is standard and does not contain the complicated combinatoric rules characteristic of most of the known variants of the diagram techniques for spin systems. The effective action for the almost antiferromagnetic Kondo lattice is derived.