The Majorana Fermions for Quantum S=1/2 Antiferromagnet?

TL;DR

This paper critically examines the proposal that Majorana fermions can irreducibly describe quantum S=1/2 antiferromagnets, demonstrating that the representation is actually highly reducible and composed of multiple fundamental parts.

Contribution

The paper refutes the claim that Majorana fermions provide an irreducible description of quantum S=1/2 antiferromagnets, showing instead that the representation is a direct sum of four irreducible components.

Findings

Majorana fermion representation is highly reducible for S=1/2 antiferromagnets

The representation decomposes into four irreducible $su(2)$ components

Challenges previous claims of an irreducible Majorana fermion description

Abstract

Recently it has been suggested by A. M. Tsvelik that quantum S=1/2 antiferromagnet can be described by the Majorana fermions in an irreducible way and without any constraint. In contrast to this claim we shall show that this representation is highly reducible. It is a direct sum of four irreducible fundamental representations of $su(2)$ algebra.