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.

arXiv comment17 pages, 11 figures

References in corpus (50)

• The electronic properties of graphene
• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Majorana Zero Modes and Topological Quantum Computation
• Kitaev-Heisenberg Model on Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_2$IrO${}_3$
• Proximate Kitaev Quantum Spin Liquid Behaviour in α-RuCl${}_3$
• Models and Materials for Generalized Kitaev Magnetism
• Spin waves and revised crystal structure of honeycomb iridate Na2IrO3
• 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 field and axial anomaly in a Weyl semi-metal
• Notes on Anomaly Induced Transport
• Crystal structure and magnetism in $\alpha$-RuCl3: an ab-initio study
• Artificial gauge fields in materials and engineered systems
• 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
• Torsional chiral magnetic effect in Weyl semimetal with topological defect
• Site dilution in Kitaev's honeycomb model
• Quantizing Majorana Fermions in a Superconductor
• 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
• Emergent spacetime and gravitational Nieh-Yan anomaly in chiral $p+ip$ Weyl superfluids and superconductors
• Mixed axial-torsional anomaly in Weyl semimetals
• Interacting non-Abelian anyons as Majorana fermions in the honeycomb lattice model
• Spectrum of the non-abelian phase in Kitaev's honeycomb lattice model
• The Wavefunction of an Anyon
• Destabilization of magnetic order in a dilute Kitaev spin liquid candidate
• Unpaired Majorana modes on dislocations and string defects in Kitaev's honeycomb model
• Torsional Landau levels and geometric anomalies in condensed matter Weyl systems
• Landau levels of Majorana fermions in a spin liquid
• Non-Abelian statistics as a Berry phase in exactly solvable models
• Lattice gauge theory model for graphene
• Topological phase transitions driven by gauge fields in an exactly solvable model
• Probing topological superconductors with emergent gravity
• Demonstrating non-Abelian statistics of Majorana fermions using twist defects
• Simulating Dirac fermions with Abelian and non-Abelian gauge fields in optical lattices
• Unpaired Majorana modes in the gapped phase of Kitaev's honeycomb model
• Thermally induced metallic phase in a gapped quantum spin liquid - a Monte Carlo study of the Kitaev model with parity projection
• Geometric description of the Kitaev honeycomb lattice model
• Hierarchical Majoranas in a Programmable Nanowire Network
• Dynamical structure factor in the non-Abelian phase of the Kitaev honeycomb model in the presence of quenched disorder
• Yang-Mills gauge theories from fermionic lattice models
• Lattice Gauge Theory - A short Primer
• Fermionic dualities with axial gauge fields
• Chiral symmetry and lattice gauge theory

Cited by in corpus (4)

• Torsional Landau levels and geometric anomalies in condensed matter Weyl systems
• Non-Abelian statistics with mixed-boundary punctures on the toric code
• Anyon condensation and confinement transition in a Kitaev spin liquid bilayer
• Geometric and computational aspects of chiral topological quantum matter