Protection against Spin Gap in 2-d Insulating Antiferromagnets with a Chern-Simons Term

TL;DR

This paper introduces a mechanism involving a Chern-Simons term that protects against spin gapped states in doped antiferromagnets, with potential experimental verification in real materials.

Contribution

It demonstrates how a Chern-Simons term induces anyonic vortex excitations and explores conditions preventing spin gap formation in antiferromagnets.

Findings

Vortex loops behave as anyons with fractional statistics

Realistic parameters prevent anyonic vortex condensation

Proposed magnetic materials for experimental testing

Abstract

We propose a novel mechanism for the protection against spin gapped states in doped antiferromagnets. It requires the presence of a Chern-Simons term that can be generated by a coupling between spin and an insulator. We first demonstrate that in the presence of this term the vortex loop excitations of the spin sector behave as anyons with fractional statistics. To generate such term, the fermions should have massive Dirac spectrum coupled to the emergent spin field of the spin sector. The Dirac spectrum can be realized by a planar spin configuration arising as the lowest-energy configuration of a square lattice antiferromagnet Hamiltonian involving a Dzyaloshinskii-Moriya interaction. The mass is provided by a combination of dimerization and staggered chemical potential. We finally show that for realistic parameters, anyonic vortex loop condensation will likely never occur and thus the spin gapped state is prevented. We also propose real magnetic materials for an experimental verification of our theory.