Emergent Fermions and Anyons in the Kitaev Model

Abstract

We study the gapped phase of the Kitaev model on the honeycomb lattice using perturbative continuous unitary transformations. The effective low-energy Hamiltonian is found to be an extended toric code with interacting anyons. High-energy excitations are emerging free fermions which are composed of hardcore bosons with an attached string of spin operators. The excitation spectrum is mapped onto that of a single particle hopping on a square lattice in a magnetic field. We also illustrate how to compute correlation functions in this framework. The present approach yields analytical perturbative results in the thermodynamical limit without using the Majorana or the Jordan-Wigner fermionization initially proposed to solve this problem.

4 pages, 5 figures, published version

References in corpus (4)

• 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
• Majorana Fermions, Exact Mappings between Classical and Topological Orders

Cited by in corpus (28)

• Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model
• Spin-S Kitaev model: Classical Ground States, Order by Disorder and Exact Correlation Functions
• Quench dynamics and defect production in the Kitaev and extended Kitaev models
• A $\Gamma$-matrix generalization of the Kitaev model
• Perturbative approach to an exactly solved problem: the Kitaev honeycomb model
• Creation and Manipulation of Anyons in the Kitaev 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
• Thermodynamic singularities in the entanglement entropy at a 2D quantum critical point
• Topological degeneracy and vortex manipulation in Kitaev's honeycomb model
• Effective models for gapped phases of strongly correlated quantum lattice models
• An exactly soluble model with tunable p-wave paired fermion ground states
• Quantum robustness and phase transitions of the 3D Toric Code in a field
• Reduced fidelity in Kitaev honeycomb model
• Instabilities of spin-1 Kitaev spin liquid phase in presence of single-ion anisotropies
• Zero energy and chiral edge modes in a p-wave magnetic spin model
• The Zero Temperature Phase Diagram of the Kitaev Model
• Truncation errors in self-similar continuous unitary transformations
• Hyperbolic Spin Liquids
• Chiral Gapless Spin Liquid in Hyperbolic Space
• Quantum phase transition as an interplay of Kitaev and Ising interactions
• Quantum phase transitions in the $K$-layer Ising toric code
• An anyon model in a toric honeycomb lattice
• Dynamic structure factor of the antiferromagnetic Kitaev model in large magnetic fields
• Exact weak bosonic zero modes in a spin/fermion chain
• Equivalence between vortices, twists and chiral gauge fields in Kitaev's honeycomb lattice model
• Sub-symmetry Protected Topology in Topological Insulators and Superconductors