The Wavefunction of an Anyon

Abstract

We consider a two-dimensional spin system in a honeycomb lattice configuration that exhibits anyonic and fermionic excitations [Kitaev, cond-mat/0506438]. The exact spectrum that corresponds to the translationally invariant case of a vortex-lattice is derived from which the energy of a single pair of vortices can be estimated. The anyonic properties of the vortices are demonstrated and their generation and transportation manipulations are explicitly given. A simple interference experiment with six spins is proposed that can reveal the anyonic statistics of this model.

8 pages, 5 figures

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Cited by in corpus (44)

• Non-Abelian Anyons and Topological Quantum Computation
• Multi-photon entanglement and interferometry
• Fidelity approach to quantum phase transitions
• Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections
• Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model
• The Bond-Algebraic Approach to Dualities
• Anyonic interferometry and protected memories in atomic spin lattices
• Bravyi-Kitaev Superfast simulation of fermions on a quantum computer
• Bond Algebras and Exact Solvability of Hamiltonians: Spin S=1/2 Multilayer Systems and Other Curiosities
• Topological states and braiding statistics using quantum circuits
• Mosaic spin models with topological order
• Perturbative approach to an exactly solved problem: the Kitaev honeycomb model
• Emulating anyonic fractional statistical behavior in a superconducting quantum circuit
• Creation and Manipulation of Anyons in the Kitaev Model
• Why should anyone care about computing with anyons?
• Topological liquid nucleation induced by vortex-vortex interactions in Kitaev's honeycomb model
• Minimum instances of topological matter in an optical plaquette
• A Description of Kitaev's Honeycomb Model with Toric-Code Stabilizers
• Interacting non-Abelian anyons as Majorana fermions in the honeycomb lattice model
• Fidelity in topological quantum phases of matter
• Detecting Majorana bound states
• Dynamical properties of hard-core anyons in one-dimensional optical lattices
• Topological degeneracy and vortex manipulation in Kitaev's honeycomb model
• Perturbed vortex lattices and the stability of nucleated topological phases
• Non-Abelian statistics as a Berry phase in exactly solvable models
• Kaleidoscope of topological phases with multiple Majorana species
• Topological phase transitions driven by gauge fields in an exactly solvable model
• Ground state properties of hard-core anyons in a harmonic potential
• Seeing Majorana fermions in time-of-flight images of spinless fermions coupled by s-wave pairing
• Zero energy and chiral edge modes in a p-wave magnetic spin model
• Topological quantum error correction in the Kitaev honeycomb model
• Diagnosing Topological Edge States via Entanglement Monogamy
• A complete characterization of the spectrum of the Kitaev model on spin ladders
• On the Strong Subadditivity of the Rényi entropies for bosonic and fermionic Gaussian states
• Anyonic Quantum Walks
• Macroscopic Quantum Tunneling Effect of Z2 Topological Order
• Anatomy of Fermionic Entanglement and Criticality in Kitaev Spin Liquids
• The Zero Temperature Phase Diagram of the Kitaev Model
• Realization of Topological Quantum Computation with surface codes
• Simulation of non-Abelian Anyons using ribbon operators connected to a common base site
• One-dimensional hard-core anyon gas in a harmonic trap at finite temperature
• Kitaev model in regular hyperbolic tilings
• Equivalence between vortices, twists and chiral gauge fields in Kitaev's honeycomb lattice model
• Quasi-particle propagation in quantum Hall systems