Non-Abelian Chiral Spin Liquid on the Kagome Lattice

Abstract

We study $S=1$ spin liquid states on the kagome lattice constructed by Gutzwiller-projected $p_x+i{p}_y$ superconductors. We show that the obtained spin liquids are either non-Abelian or Abelian topological phases, depending on the topology of the fermionic mean-field state. By calculating the modular matrices $S$ and $T$, we confirm that projected topological superconductors are non-Abelian chiral spin liquid (NACSL). The chiral central charge and the spin Hall conductance we obtained agree very well with the $SO(3{)}_1$ (or, equivalently, $SU(2{)}_2$) field theory predictions. We propose a local Hamiltonian which may stabilize the NACSL. From a variational study we observe a topological phase transition from the NACSL to the $Z_2$ Abelian spin liquid.

12 pages, 7 figures, 1 table

References in corpus (18)

• Non-Abelian Anyons and Topological Quantum Computation
• Quantum Spin Liquid States
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Gapless spin-liquid ground state in the $S=1/2$ kagome antiferromagnet
• Global Phase Diagram of Competing Ordered and Quantum Spin Liquid Phases on the Kagomé Lattice
• A theory of 2+1D bosonic topological orders
• Non-Abelian Statistics in a Quantum Antiferromagnet
• Quantized topological terms in weak-coupling gauge theories with symmetry and their connection to symmetry enriched topological phases
• Nature of chiral spin liquids on the kagome lattice
• Symmetry protected Spin Quantum Hall phases in 2-Dimensions
• Paired chiral spin liquid with a Fermi surface in S=1 model on the triangular lattice
• Global phase diagram, possible chiral spin liquid and topological superconductivity in the triangular Kitaev-Heisenberg model
• Simplex valence-bond crystal in the spin-1 kagome Heisenberg antiferromagnet
• Projected BCS states and spin Hamiltonians for the SO(n)_1 Wess-Zumino-Witten model
• Exact parent Hamiltonians of bosonic and fermionic Moore-Read states on lattices and local models
• Fermionic theory for quantum antiferromagnets with spin S > 1/2
• $U(1)\times U(1)$ Symmetry Protected Topological Order in Gutzwiller Wave Functions
• Hexagon-singlet solid ansatz for the spin-1 kagome antiferromagnet

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• Recent progress in quantum spin liquids, fractional magnetization plateaus, and unconventional superconductivity in kagome lattices
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