Supersymmetric approach to heavy fermion systems

TL;DR

This paper introduces a supersymmetric framework with symplectic symmetry for modeling heavy fermion systems, applying it to toy models to explore the competition between Kondo effect and antiferromagnetism.

Contribution

It generalizes the supersymmetric spin representation from SU(2) to SP(N), enabling new analysis of heavy fermion phenomena and their phase competition.

Findings

Demonstrated the applicability of the new representation to toy models.

Explored the energetic favorability of different representations in parameter space.

Discussed potential extensions to Kondo lattice models.

Abstract

We propose a generalization of the supersymmetric representation of spins with symplectic symmetry, generalizing the rotation group of the spin from SU(2) to SP(N). As a test application of this new representation, we consider two toy models involving a competition of the Kondo effect and antiferromagnetism: a two-impurity model and a frustrated three-impurity model. Exploring an ensemble of L-shaped representations with a fixed number of boxes in their respective Young tableaux, we allow the system to choose which representation is energetically more favorable in each region in parameter space. We discuss how the features of these preliminary applications can generalize to Kondo lattice models.