A dynamical Toric Code model with fusion and de-fusion

Abstract

We introduce a two-parameter family of perturbations of Kitaev's Toric Code Model in which the anyonic excitations acquire an interesting dynamics. We study the dynamics of this model in the space of states with electric and magnetic charge both equal to 1 and find that the model exhibits both bound states and scattering states in a suitable region of the parameters. The bound state is a Majorana fermion with a dispersion relation of Dirac cone type. For a certain range of model parameters, we find that these bound states disappear in a continuum of scattering states at a critical value of the total momentum. The scattering states describe separate electric and magnetic anyons, which in this model each have a sin k dispersion relation.

References in corpus (17)

• Fault-tolerant quantum computation by anyons
• String-net condensation: A physical mechanism for topological phases
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• The Rare Two-Dimensional Materials with Dirac Cones
• Topological quantum order: stability under local perturbations
• Observation of Chiral Fermions with a Large Topological Charge and and Associated Fermi-Arc Surface States in CoSi
• A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
• Fracton Models on General Three-Dimensional Manifolds
• Magnetic field-tuned Aharonov-Bohm oscillations and evidence for non-Abelian anyons at v=5/2
• Charged fermions coupled to ${\mathbb{Z}}_2$ gauge fields: Superfluidity, confinement and emergent Dirac fermions
• A statistical mechanics view on Kitaev's proposal for quantum memories
• Statistics of fractionalized excitations through threshold spectroscopy
• Localized endomorphisms in Kitaev's toric code on the plane
• On the stability of topological phases on a lattice
• On the stability of charges in infinite quantum spin systems
• The complete set of infinite volume ground states for Kitaev's abelian quantum double models
• Fractional Chern insulator edges and layer-resolved lattice contacts

Cited by in corpus (4)

• Stability of invertible, frustration-free ground states against large perturbations
• Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States
• Dynamical abelian anyons with bound states and scattering states
• A Computer Code for Topological Quantum Spin Systems over Triangulated Surfaces