Anyonic Loops in Three Dimensional Spin liquid and Chiral Spin Liquid

Abstract

We established a large class of exactly soluble spin liquids and chiral spin liquids on three dimensional helix lattices by introducing Kitaev-type's spin coupling. In the chiral spin liquids, exact stable ground states with spontaneous breaking of the time reversal symmetry are found. The fractionalized loop excitations in both the spin and chiral spin liquids obey non-abelian statistics. We characterize this kind of statistics by non-abelian Berry phase and quantum algebra relation. The topological correlation of loops is independent of local order parameter and it measures the intrinsic global quantum entanglement of degenerate ground states.

13 pages, 12 figures, final version to be published on Nucl. Phys. B

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• Topological Quantum Distillation
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• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
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• Physical states and finite-size effects in Kitaev's honeycomb model: Bond disorder, spin excitations, and NMR lineshape
• Theory of Magnetic Phase Diagrams in Hyperhoneycomb and Harmonic-honeycomb Iridates
• A $\Gamma$-matrix generalization of the Kitaev model
• Three-dimensional topological phase on the diamond lattice
• Fractional topological phases in three-dimensional coupled-wire systems
• Crystalline Kitaev spin liquids
• Kaleidoscope of topological phases with multiple Majorana species
• Classical Heisenberg spins on a hexagonal lattice with Kitaev couplings
• Three-dimensional topological phases in a layered honeycomb spin-orbital model
• Topological Color Codes and Two-Body Quantum Lattice Hamiltonians
• Spin-1 Kitaev model in one dimension
• Generalized Toric Codes Coupled to Thermal Baths
• Generic Field-Driven Phenomena in Kitaev Spin Liquids: Canted Magnetism and Proximate Spin Liquid Physics
• Thermodynamics of 3D Kitaev quantum spin liquids via tensor networks
• Topological excitations in three dimensional Kitaev model
• An exactly solvable dissipative spin liquid
• Compass and Kitaev models -- Theory and Physical Motivations
• Chiral Spin Liquids at Finite Temperature in a Three-Dimensional Kitaev Model
• Improved Honeycomb and Hyperhoneycomb Lattice Hamiltonians for Quantum Simulations of Non-Abelian Gauge Theories
• Pristine Mott Insulator from an Exactly Solvable Spin-1/2 Kitaev Model
• Bound states of fractionalized excitations in a modulated Kitaev spin liquid
• Entangled multi-knot lattice model of anyon current
• Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via coupled Heisenberg equations
• Polynomially restricted operator growth in dynamically integrable models
• Global constraints on $Z_2$ fluxes in two different anisotropic limits of a hypernonagon Kitaev model
• Fractionally charged anyon generated by topological path fusion in magnetic flux lattice
• Classification and correlation signatures of chiral spin liquids on the pyrochlore lattice