Exact chiral spin liquid state in a Kitaev type spin model

Abstract

We study a frustrated two-dimensional lattice spin model with Kitaev type interaction. The lattice is obtained from the honeycomb lattice by replacing half of its sites with triangles. Using the SO(3) Majorana representation of spin, the model is exactly mapped into a $Z_2$ lattice gauge theory of complex fermions with standard Gauss law constraint. We show that the ground state of the model is a chiral spin liquid, and it has gapless excitations. The Chern number of the ground state is $\pm 1$, implying the existence of chiral edge mode. The vortex excitation of the model is bound with a Majorana zero mode, such mode behaves as non-Abelian anyons.

References in corpus (50)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Berry Phase Effects on Electronic Properties
• Anyons in an exactly solved model and beyond
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Classification of topological insulators and superconductors in three spatial dimensions
• Classification of topological quantum matter with symmetries
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Periodic table for topological insulators and superconductors
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Theory of Thermal Hall Effect in Quantum Magnets
• Exact results for spin dynamics and fractionization in the Kitaev Model
• An exact chiral spin liquid with non-Abelian anyons
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• Quantized Thermal Transport in the Fractional Quantum Hall Effect
• A Class of $P,T$-Invariant Topological Phases of Interacting Electrons
• Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model
• The kagome antiferromagnet: a chiral topological spin liquid ?
• Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Possible Quantum Spin Liquid States on the Triangular and Kagome Lattices
• Non-Abelian Statistics in a Quantum Antiferromagnet
• Stability of half-quantum vorticies in p_x+ip_y superconductors
• An Index Theorem for the Majorana Zero Modes in Chiral P-Wave Superconductors
• New Fermionic Description of Quantum S = 1/2 Antiferromargnet
• Parent Hamiltonian for the non-Abelian chiral spin liquid
• Parent Hamiltonian for the Chiral Spin Liquid
• Exact Chiral Spin Liquid with Stable Spin Fermi Surface on the Kagome Lattice
• Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking
• Spin-spin correlators in Majorana representation
• SU(2)-invariant spin liquids on the triangular lattice with spinful Majorana excitations
• Spin dynamics from Majorana fermions
• Topological Majorana and Dirac zero modes in superconducting vortex cores
• Coexisting edge states and gapless bulk in topological states of matter
• Lattice spin models for non-Abelian Chiral Spin Liquids
• Thermodynamics of Chiral Spin Liquids with Abelian and Non-Abelian Anyons
• Majorana representations of spin and an alternative solution of the Kitaev honeycomb model
• Nature of a topological quantum phase transition in a chiral spin liquid model
• SU(2)-invariant Majorana spin liquid with stable parton Fermi surfaces in an exactly solvable model
• Exact results for the star lattice chiral spin liquid
• Exactly Solvable Topological Chiral Spin Liquid with Random Exchange
• Chiral liquid phase of simple quantum magnets
• Gapless Topological Superconductors - Model Hamiltonian and Realization
• Exotic phase diagram of a topological quantum system
• Properties and application of the SO(3) Majorana representation of spin: equivalence with the Jordan-Wigner transformation and exact $Z_2$ gauge theories for spin models

Cited by in corpus (7)

• Non-Abelian chiral spin liquid on a simple non-Archimedean lattice
• Eight-color chiral spin liquid in the $S=1$ bilinear-biquadratic model with Kitaev interactions
• Exact weak bosonic zero modes in a spin/fermion chain
• Continuous phase transition from a chiral spin state to collinear magnetic order in a zigzag chain with Kitaev interactions
• Effective models for dense vortex lattices in the Kitaev honeycomb model
• Floquet dynamical chiral spin liquid at finite frequency
• Theory of collective topologically-protected Majorana fermion excitations of networks of localized Majorana modes