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

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.

To appear in Physical Review B

References in corpus (4)

• Scalar spin chirality and quantum Hall effect on a triangular lattice
• A discretized Chern-Simons gauge theory on arbitrary graphs
• Chern-Simons theory of the magnetization plateaus of the spin-1/2 quantum XXZ Heisenberg model on Kagome Lattice
• Geometric phases and the magnetization process in quantum antiferromagnets

Cited by in corpus (4)

• From frustrated magnetism to spontaneous Chern insulators
• On Anderson Localization and Chiral Anomaly in Disordered Time-Reversal Invariant Weyl Semimetals: Nonperturbative and Berry Phase Effects
• Quantum Anomalous Hall Effect in $d$-Electron Kagome Systems: Chern Insulating States from Transverse Spin-Orbit Coupling
• Effective Field Theory of Chiral Spin Liquid between Ordered Phases in Kagomé Antiferromagnet