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.

arXiv comment15 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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• Signatures of a spin-1/2 cooperative paramagnet in the diluted triangular lattice of Y${}_2$CuTiO${}_6$
• Demonstrating non-Abelian statistics of Majorana fermions using twist defects
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• Globally symmetric topological phase: from anyonic symmetry to twist defect
• Majorana Spin Liquids, Topology and Superconductivity in Ladders
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• A family of stabilizer codes for $D({\mathbb{Z}}_2)$ anyons and Majorana modes
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• Vacancies in the Kitaev quantum spin liquids on the 3D hyper-honeycomb lattice
• Continuous error correction for Ising anyons
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• Projective symmetry of partons in Kitaev's honeycomb model
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• Chiral Gapless Spin Liquid in Hyperbolic Space
• Raman Scattering Polarization and Single Spinon Identification in Two-Dimensional Kitaev Quantum Spin Liquids
• Gapless excitations in non-Abelian Kitaev spin liquids with line defects
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• Equivalence between vortices, twists and chiral gauge fields in Kitaev's honeycomb lattice model
• Projective-symmetry-group analysis of inelastic light scattering in Kitaev spin balls
• Dihedral twist liquid models from emergent Majorana fermions
• Quantum spin liquid with 7 elementary particles
• 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