Non-Abelian Statistics in a Quantum Antiferromagnet

2009/03/26 by Martin Greiter, Ronny Thomale · 11 citations
Mathematics · Physics and Astronomy · #Abelian group #Advanced Condensed Matter Physics #Antiferromagnetism #Condensed matter physics #Electron #Excited state #Ground state #Hamiltonian (control theory) #Homogeneous space #Invariant (physics) #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum #Quantum many-body systems #Quantum mechanics #Quantum spin liquid #Renormalization group #Singlet state #Spin polarization #Spinon #Theoretical physics #cond-mat.str-el

paper · pdf · doi:10.1103/physrevlett.102.207203

published as Phys. Rev. Lett. 102, 207203 (2009) · 5 pages, 2 figures

arxiv created 2009/03/26 · openalex publication_date 2009/05/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We propose a novel spin liquid state for a spin S = 1 antiferromagnet in two dimensions. The ground state violates P and T, is a spin-singlet, and is fully invariant under the lattice symmetries. The spinon and holon excitations are deconfined and obey non-Abelian statistics. We present preliminary numerical evidence that the universality class of this topological liquid can be stabilized by a local Hamiltonian involving three-spin interactions.

Citations

• Pfaffian-like ground state for three-body hard-core bosons in one-dimensional lattices
• Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations
• Quantum Mechanics of Fractional-Spin Particles
• Equivalence of the resonating-valence-bond and fractional quantum Hall states
• Anyons in an exactly solved model and beyond
• Non-Abelian anyons and topological quantum computation
• Nonabelions in the fractional quantum hall effect

Cited by

• Conformal field theory and the non-abelian SU(2)_k chiral spin liquid
• Parent Hamiltonian Construction of Generalized Calogero-Sutherland Models
• Exact parent Hamiltonians of bosonic and fermionic Moore–Read states on lattices and local models
• Resonating valence bond realization of spin-1 non-Abelian chiral spin liquid on the torus
• A quantum dipolar spin liquid
• Chiral Projected Entangled-Pair State with Topological Order
• Topologically driven three-spin chiral exchange interactions treated from first principles
• Quantum spin liquid states
• Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry
• Realizing Fractional Chern Insulators in Dipolar Spin Systems
• Mott insulators of ultracold fermionic alkaline earth atoms in three dimensions

Related

• S=1 Spin Liquids: Broken Discrete Symmetries Restored
• Quantum Antiferromagnets in Two Dimensions
• An exact chiral spin liquid with non-Abelian anyons
• Theory of Dirac spin liquids on spin-S triangular lattice: possible application to α-CrOOH(D)
• Two-orbital Schwinger Boson Representation of Spin-One: Application to a Non-abelian Spin Liquid with Quaternion Gauge Field