The Kondo Lattice Model

TL;DR

This paper reviews the Kondo lattice model's role in describing heavy Fermion systems, focusing on quantum phase transitions and non-Fermi liquid behavior, and introduces two novel theoretical approaches to better understand these phenomena.

Contribution

It presents two new theoretical frameworks—spin fluctuation-Kondo functional integral and supersymmetric theory—for analyzing quantum criticality in heavy Fermion systems.

Findings

New approaches treat spin fluctuations and Kondo effects simultaneously.

Potential to improve understanding of quantum phase transitions.

Frameworks may lead to better descriptions of non-Fermi liquid behavior.

Abstract

In this lecture, we review the experimental situation of heavy Fermions with emphasis on the existence of a quantum phase transition (QPT) and related non-Fermi liquid (NFL) effects. We overview the Kondo lattice model (KLM) which is believed to describe the physics of those systems. After recalling the existing theories based on large-N expansion and various N=2 schemes, we present two alternative approaches: (i) a spin fluctuation-Kondo functional integral approach treating the spin-fluctuation and Kondo effects on an equal footing, and (ii) a supersymmetric theory enlarging the usual fermionic representation of the spin into a mixed fermionic-bosonic representation in order to describe the spin degrees of freedom as well as the Fermi-liquid type excitations. This kind of approaches may open up new prospects for the description of the critical phenomena associated to the quantum phase transition in Heavy-Fermion systems.