Anyons in integer quantum Hall magnets

Abstract

Strongly correlated fractional quantum Hall liquids support fractional excitations, which can be understood in terms of adiabatic flux insertion arguments. A second route to fractionalization is through the coupling of weakly interacting electrons to topologically nontrivial backgrounds such as in polyacetylene. Here we demonstrate that electronic fractionalization combining features of both these mechanisms occurs in noncoplanar itinerant magnetic systems, where integer quantum Hall physics arises from the coupling of electrons to the magnetic background. The topologically stable magnetic vortices in such systems carry fractional (in general irrational) electronic quantum numbers and exhibit Abelian anyonic statistics. We analyze the properties of these topological defects by mapping the distortions of the magnetic texture onto effective non-Abelian vector potentials. We support our analytical results with extensive numerical calculations.

15 pages, 12 figures, supersedes arXiv:1112.3347, to be published in PRX

References in corpus (12)

• Topological Defects and Gapless Modes in Insulators and Superconductors
• Topological Mott Insulators
• Electron fractionalization in two-dimensional graphenelike structures
• Scalar spin chirality and quantum Hall effect on a triangular lattice
• Theory of defects in Abelian topological states
• Classification of Topological Defects in Abelian Topological States
• Electron fractionalization for two-dimensional Dirac fermions
• Frustration-induced insulating chiral spin state in itinerant triangular-lattice magnets
• Noncoplanar magnetic ordering driven by itinerant electrons on the pyrochlore lattice
• Unconventional Fusion and Braiding of Topological Defects in a Lattice Model
• Fractional statistics of topological defects in graphene and related structures
• Creation and manipulation of anyons in a layered superconductor-2DEG system

Cited by in corpus (12)

• Emergence of Chiral Spin Liquids via Quantum Melting of Non-Coplanar Magnetic Orders
• Topological semimetal-to-insulator phase transition between noncollinear and noncoplanar multiple-Q states on a square-to-triangular lattice
• Spontaneous formation of kagome network and Dirac half-semimetal on a triangular lattice
• Noncollinear magnetic ordering in a frustrated magnet: Metallic regime and the role of frustration
• Topological Green function of interacting systems
• Dynamics of noisy quantum systems in the Heisenberg picture: application to the stability of fractional charge
• Antiferromagnetic chiral spin density wave and strain-induced Chern insulator in the square lattice Hubbard model with frustration
• Berry phase in the rigid rotor: the emergent physics of odd antiferromagnets
• Phase Diagram of the Shastry-Sutherland Kondo Lattice Model with Classical Localized Spins: A Variational Calculation Study
• Synthetic anyons in noninteracting systems
• An exactly solvable model for anyons with non-Abelian flux
• ${\mathbb{Z}}_2$ Vortex Crystals in Tetrahedral Antiferromagnets: Fractional Charges and Topological Magnons