Majorana Fermion Representation For An Antiferromagnetic Spin-1/2 Chain

TL;DR

This paper introduces a Majorana fermion representation for the 1D Heisenberg antiferromagnetic spin-1/2 chain, providing a rotationally invariant fermionic description that captures power-law correlations and spin-1 excitations.

Contribution

It presents a novel Majorana fermion framework for the spin-1/2 chain, offering insights into correlations and excitations beyond traditional spinon models.

Findings

Power-law correlations in the ground state

Two-parameter family of spin-1 excitations

Rotationally invariant fermionic description

Abstract

We study the 1-dimensional Heisenberg antiferromagnet with s=1/2 using a Majorana representation of the s=1/2 spins. A simple Hartree-Fock approximation of the resulting model gives a bilinear fermionic description of the model. This description is rotationally invariant and gives power-law correlations in the ``ground state'' in a natural fashion. The excitations are a two-parameter family of particles, which are spin-1 objects. These are contrasted to the ``spinon'' spectrum, and the technical aspects of the representation are discussed, including the problem of redundant states.