Unpaired Majorana modes on dislocations and string defects in Kitaev's honeycomb model

Abstract

We study the gapped phase of Kitaev's honeycomb model (a $Z_2$ spin liquid) on a lattice with topological defects. We find that some dislocations and string defects carry unpaired Majorana fermions. Physical excitations associated with these defects are (complex) fermion modes made out of two (real) Majorana fermions connected by a $Z_2$ gauge string. The quantum state of these modes is robust against local noise and can be changed by winding a $Z_2$ vortex around one of the dislocations. The exact solution respects gauge invariance and reveals a crucial role of the gauge field in the physics of Majorana modes. To facilitate these theoretical developments, we recast the degenerate perturbation theory for spins in the language of Majorana fermions.

15 pages, 7 figures; added a brief history of twists, references, and clarified the count of the topological degeneracy of the ground state

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Cited by in corpus (17)

• Theory of Twist Liquids: Gauging an Anyonic Symmetry
• Thermodynamic and Transport Properties in Disordered Kitaev Models
• Signatures of a spin-1/2 cooperative paramagnet in the diluted triangular lattice of Y${}_2$CuTiO${}_6$
• Topological flat bands in time-periodically driven uniaxial strained graphene nanoribbons
• A family of stabilizer codes for $D({\mathbb{Z}}_2)$ anyons and Majorana modes
• Kitaev model on Hurwitz hyperbolic tilings: A non-Abelian gapped chiral spin liquid
• Projective symmetry of partons in Kitaev's honeycomb model
• Anyon condensation and confinement transition in a Kitaev spin liquid bilayer
• Raman Scattering Polarization and Single Spinon Identification in Two-Dimensional Kitaev Quantum Spin Liquids
• Generalizations of Kitaev's honeycomb model from braided fusion categories
• Chiral Gapless Spin Liquid in Hyperbolic Space
• Kitaev model in regular hyperbolic tilings
• Projective-symmetry-group analysis of inelastic light scattering in Kitaev spin balls
• Equivalence between vortices, twists and chiral gauge fields in Kitaev's honeycomb lattice model
• The Kitaev honeycomb model on surfaces of genus $g\ge 2$
• Real-space chirality from crystalline topological defects in the Kitaev spin liquid
• Tunable anyonic permeability across ${\mathbb{Z}}_2$ spin liquid junctions