Interacting non-Abelian anyons as Majorana fermions in the honeycomb lattice model

Abstract

We study the collective states of interacting non-Abelian anyons that emerge in Kitaev's honeycomb lattice model. Vortex-vortex interactions are shown to lead to the lifting of the topological degeneracy and the energy is discovered to exhibit oscillations that are consistent with Majorana fermions being localized at vortex cores. We show how to construct states corresponding to the fusion channel degrees of freedom and obtain the energy gaps characterizing the stability of the topological low energy spectrum. To study the collective behavior of many vortices, we introduce an effective lattice model of Majorana fermions. We find necessary conditions for it to approximate the spectrum of the honeycomb lattice model and show that bi-partite interactions are responsible for the degeneracy lifting also in many vortex systems.

22 pages, 12 figures, published version

References in corpus (21)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Interacting anyons in topological quantum liquids: The golden chain
• An exact chiral spin liquid with non-Abelian anyons
• Possible proximity of the Mott insulating Iridate Na2IrO3 to a topological phase: Phase diagram of the Heisenberg-Kitaev model in a magnetic field
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Splitting of Majorana modes due to intervortex tunneling in a p + ip superconductor
• Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions
• Tunneling of anyonic Majorana excitations in topological superconductors
• Zero modes of two-dimensional chiral p-wave superconductors
• Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
• Numerical Analysis of Quasiholes of the Moore-Read Wavefunction
• Perturbative approach to an exactly solved problem: the Kitaev honeycomb model
• Why should anyone care about computing with anyons?
• A Description of Kitaev's Honeycomb Model with Toric-Code Stabilizers
• The Wavefunction of an Anyon
• Topological degeneracy and vortex manipulation in Kitaev's honeycomb model
• Splitting and oscillation of Majorana zero modes in the p-wave BCS-BEC evolution with plural vortices
• Non-Abelian statistics as a Berry phase in exactly solvable models
• An exactly soluble model with tunable p-wave paired fermion ground states
• Zero energy and chiral edge modes in a p-wave magnetic spin model

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• Thermally induced metallic phase in a gapped quantum spin liquid - a Monte Carlo study of the Kitaev model with parity projection
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• Dynamical structure factor in the non-Abelian phase of the Kitaev honeycomb model in the presence of quenched disorder
• Kane-Mele-Hubbard model on the $\pi$-flux honeycomb lattice
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• Effect of thermal fluctuations in topological p-wave superconductors
• Anatomy of Fermionic Entanglement and Criticality in Kitaev Spin Liquids
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• Quantum subspace expansion approach for simulating dynamical response functions of Kitaev spin liquids
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• Digital Quantum Simulation of the Kitaev Quantum Spin Liquid
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• Effective models for dense vortex lattices in the Kitaev honeycomb model
• Real-time control of non-Abelian anyons in Kitaev spin liquid under energy dissipation
• Magnetic Susceptibility of Dirac Fermions, Bi-Sb Alloys, Interacting Bloch Fermions, Dilute Nonmagnetic Alloys, and Kondo Alloys
• The Kekulé-Kitaev model: linear and non-linear responses and magnetic field effects
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