Realization of the Exactly Solvable Kitaev Honeycomb Lattice Model in a Spin Rotation Invariant System

Abstract

The exactly solvable Kitaev honeycomb lattice model is realized as the low energy effect Hamiltonian of a spin-1/2 model with spin rotation and time-reversal symmetry. The mapping to low energy effective Hamiltonian is exact, without truncation errors in traditional perturbation series expansions. This model consists of a honeycomb lattice of clusters of four spin-1/2 moments, and contains short-range interactions up to six-spin(or eight-spin) terms. The spin in the Kitaev model is represented not as these spin-1/2 moments, but as pseudo-spin of the two-dimensional spin singlet sector of the four antiferromagnetically coupled spin-1/2 moments within each cluster. Spin correlations in the Kitaev model are mapped to dimer correlations or spin-chirality correlations in this model. This exact construction is quite general and can be used to make other interesting spin-1/2 models from spin rotation invariant Hamiltonians. We discuss two possible routes to generate the high order spin interactions from more natural couplings, which involves perturbative expansions thus breaks the exact mapping, although in a controlled manner.

11 pages, 3 figure, 1 table, RevTex4, rewritten for clarity, error corrected, references added.

References in corpus (18)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• An exact chiral spin liquid with non-Abelian anyons
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Emergent Fermions and Anyons in the Kitaev Model
• Mechanisms of degeneracy breaking in pyrochlore antiferromagnets
• A $\Gamma$-matrix generalization of the Kitaev model
• Spin phonon induced colinear order and magnetization plateaus in triangular and kagome antiferromagnets. Applications to CuFeO_2
• Parent Hamiltonian for the Chiral Spin Liquid
• Perturbative approach to an exactly solved problem: the Kitaev honeycomb model
• Three-dimensional topological phase on the diamond lattice
• Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking
• A Description of Kitaev's Honeycomb Model with Toric-Code Stabilizers
• Broken parity and a chiral ground state in the frustrated magnet CdCr2O4
• Chiral entanglement in triangular lattice models
• An exactly soluble model with tunable p-wave paired fermion ground states

Cited by in corpus (15)

• Quantum Spin Liquid States
• Fermionic magnons, non-Abelian spinons, and spin quantum Hall effect from an exactly solvable Kitaev Hamiltonian with SU(2) symmetry
• Finite-size scaling and boundary effects in two-dimensional valence-bond-solids
• SU(2)-invariant spin liquids on the triangular lattice with spinful Majorana excitations
• Towards Kitaev Spin Liquid in 3d Transition Metal Compounds
• Changing topology by topological defects in three-dimensional topologically ordered phases
• Topological Insulators and Quantum Spin Liquids
• Majorana spin liquids and projective realization of SU(2) spin symmetry
• Exact resummation of the Holstein-Primakoff expansion and differential equation approach to operator square-roots
• Edge magnetization and spin transport in an SU(2)-symmetric Kitaev spin liquid
• SU(2)-invariant Majorana spin liquid with stable parton Fermi surfaces in an exactly solvable model
• Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware
• Power-Law Behavior of Bond Energy Correlators in a Kitaev-type Model with a Stable Parton Fermi Surface
• Compass and Kitaev models -- Theory and Physical Motivations
• Pristine Mott Insulator from an Exactly Solvable Spin-1/2 Kitaev Model