Equivalence between vortices, twists and chiral gauge fields in Kitaev's honeycomb lattice model

Abstract

We demonstrate that ${\mathbb{Z}}_2$ gauge transformations and lattice deformations in Kitaev's honeycomb lattice model can have the same description in the continuum limit of the model in terms of chiral gauge fields. The chiral gauge fields are coupled to the Majorana fermions that satisfy the Dirac dispersion relation in the non-Abelian sector of the model. For particular values, the effective chiral gauge field becomes equivalent to the ${\mathbb{Z}}_2$ gauge field, enabling us to associate effective fluxes to lattice deformations. Motivated by this equivalence, we consider Majorana-bounding $\pi$ vortices and Majorana-bounding lattice twists and demonstrate that they are adiabatically connected to each other. This equivalence opens the possibility for novel encoding of Majorana-bounding defects that might be easier to realise in experiments.

17 pages, 11 figures

References in corpus (19)

• The electronic properties of graphene
• Non-Abelian Anyons and Topological Quantum Computation
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Models and Materials for Generalized Kitaev Magnetism
• Electron fractionalization in two-dimensional graphenelike structures
• AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Chiral Gauge Theory for Graphene
• Chiral anomaly from strain-induced gauge fields in Dirac and Weyl semimetals
• Inhomogeneous Weyl and Dirac semimetals: Transport in axial magnetic fields and Fermi arc surface states from pseudo Landau levels
• Emergent Fermions and Anyons in the Kitaev Model
• Consistent Chiral Kinetic Theory in Weyl Materials: Chiral Magnetic Plasmons
• Creation and Manipulation of Anyons in the Kitaev Model
• The Wavefunction of an Anyon
• Unpaired Majorana modes on dislocations and string defects in Kitaev's honeycomb model
• Non-Abelian statistics as a Berry phase in exactly solvable models
• Lattice gauge theory model for graphene
• Yang-Mills gauge theories from fermionic lattice models
• Fermionic dualities with axial gauge fields

Cited by in corpus (1)

• Geometric and computational aspects of chiral topological quantum matter