Majorana fermion representation for an antiferromagnetic spin-½ chain

Abstract

We study the 1-dimensional Heisenberg antiferromagnet with s= ½ using a Majorana representation of the s= ½ 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.