Majorana fermion description of the Kondo lattice: Variational and Path integral approach

TL;DR

This paper reformulates the Kondo lattice model using Majorana fermions, exploring variational states at different couplings and developing a path integral formalism for further analytical and numerical studies.

Contribution

It introduces a Majorana fermion-based variational approach to the Kondo lattice and derives a general path integral formulation for Majorana theories.

Findings

Weak coupling favors bound Majorana states

Strong coupling favors deconfined Majorana fermions

Path integral formalism enables advanced analysis methods

Abstract

All models of interacting electrons and spins can be reformulated as theories of interacting Majorana fermions. We consider the Kondo lattice model that admits a symmetric representation in terms of Majorana fermions. In the first part of this work we study two variational states, which are natural in the Majorana formulation. At weak coupling a state in which three Majorana fermions tend to propagate together as bound objects is favored, while for strong coupling a better description is obtained by having deconfined Majorana fermions. This way of looking at the Kondo lattice offers an alternative phenomenological description of this model. In the second part of the paper we provide a detailed derivation of the discretized path integral formulation of any Majorana fermion theory. This general formulation will be useful as a starting point for further studies, such as Quantum Monte Carlo, perturbative expansions, and Renormalization Group analysis. As an example we use this path integral formalism to formulate a finite temperature variational calculation, which generalizes the ground state variational calculation of the first part. This calculation shows how the formation of three-body bound states of Majorana fermions can be handled in the path integral formalism.