Non-Abelian statistics of vortices with multiple Majorana fermions

Abstract

We consider the exchange statistics of vortices, each of which traps an odd number ($N$) of Majorana fermions. We assume that the fermions in a vortex transform in the vector representation of the SO(N) group. Exchange of two vortices turns out to be non-Abelian, and the corresponding operator is further decomposed into two parts: a part that is essentially equivalent to the exchange operator of vortices having a single Majorana fermion in each vortex, and a part representing the Coxeter group. Similar decomposition was already found in the case with N=3, and the result shown here is a generalization to the case with an arbitrary odd $N$. We can obtain the matrix representation of the exchange operators in the Hilbert space that is constructed by using Dirac fermions non-locally defined by Majorana fermions trapped in separated vortices. We also show that the decomposition of the exchange operator implies tensor product structure in its matrix representation.

arXiv comment23 pages; v2: published version in Phys. Rev. B

References in corpus (32)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Classification of topological insulators and superconductors in three spatial dimensions
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Color superconductivity in dense quark matter
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Fermion zero modes on vortices in chiral superconductors
• Classification of Topological Insulators and Superconductors
• Geometric phases and quantum entanglement as building blocks for nonabelian quasiparticle statistics
• Majorana Fermions and Non-Abelian Statistics in Three Dimensions
• Fusion rules and vortices in $p_x+i{p}_y$ superconductors
• Semi-superfluid strings in High Density QCD
• Non-Abelian Strings in High Density QCD: Zero Modes and Interactions
• Instabilities of Non-Abelian Vortices in Dense QCD
• Color Magnetic Flux Tubes in Dense QCD
• Color Magnetic Flux Tubes in Dense QCD. II: Effective World-Sheet Theory
• Non-Abelian Statistics of Axion Strings
• Projective Ribbon Permutation Statistics: a Remnant of non-Abelian Braiding in Higher Dimensions
• Topological Majorana and Dirac zero modes in superconducting vortex cores
• Non-Abelian Strings in Hot or Dense QCD
• Fermion structure of non-Abelian vortices in high density QCD
• Confined Monopoles Induced by Quantum Effects in Dense QCD
• Confined Magnetic Monopoles in Dense QCD
• Index theorem and Majorana zero modes along a non-Abelian vortex in a color superconductor
• Majorana meets Coxeter: Non-Abelian Majorana Fermions and Non-Abelian Statistics
• Topological Interactions of Non-Abelian Vortices with Quasi-Particles in High Density QCD
• Dirac returns: non-Abelian statistics of vortices with Dirac fermions
• Non-Abelian statistics versus the Witten anomaly
• State Space for Planar Majorana Zero Modes
• Constrained Jackiw-Rebbi model gives McGreevy-Swingle model

Cited by in corpus (18)

• Symmetry Protected Topological Superfluids and Superconductors --- From the Basics to ${}^3$He ---
• Vortices and Other Topological Solitons in Dense Quark Matter
• Quark-hadron continuity beyond Ginzburg-Landau paradigm
• Symmetry Protected Topological Superfluid ${}^3$He-B
• Quark-hadron continuity under rotation: Vortex continuity or boojum?
• Mirror Majorana zero modes in spinful superconductors/superfluids -Non-Abelian braiding of integer quantum vortices-
• Anisotropic Optical Response of Dense Quark Matter under Rotation: Compact Stars as Cosmic Polarizers
• Non-Abelian Alice strings in two-flavor dense QCD
• Microscopic description of axisymmetric vortices in ${}^3{P}_2$ superfluids
• Topological Defects in the Georgi-Machacek Model
• Topological confinement of vortices in two-flavor dense QCD
• Coupling between Majorana fermions and Nambu-Goldstone bosons inside a non-Abelian vortex in dense QCD
• Chiral non-Abelian vortices and their confinement in three flavor dense QCD
• Non-Abelian statistics of vortices with non-Abelian Dirac fermions
• The effective action of a BPS Alice string
• Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors
• Quark-Hadron Crossover with Vortices
• Chiral non-Abelian vortex molecules in dense QCD