Nonabelian braid statistics versus projective permutation statistics

Abstract

Recent papers by Finkelstein, Galiautdinov, and coworkers {[J. Math. Phys. 42, 1489, 3299 (2001)]} discuss a suggestion by Wilczek that nonabelian projective representations of the permutation group can be used as a new type of particle statistics, valid in any dimension. Wilczek's suggestion was based in part on an analysis by Nayak and Wilczek (NW) of the nonabelian representation of the braid group in a quantum Hall system. We point out that projective permutation statistics is not possible in a local quantum field theory as it violates locality, and show that the NW braid group representation is not equivalent to a projective representation of the permutation group. The structure of the finite image of the braid group in a 2^{n/2-1}-dimensional representation is obtained.

4 pages, RevTeX. v. 2: added refs and some small changes

References in corpus (4)

• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Clifford algebra as quantum language
• Cliffordons

Cited by in corpus (14)

• Non-Abelian Anyons and Topological Quantum Computation
• Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
• Genons, twist defects, and projective non-Abelian braiding statistics
• Non-Abelian operations on Majorana fermions via single charge control
• Projective Ribbon Permutation Statistics: a Remnant of non-Abelian Braiding in Higher Dimensions
• Implementation of Clifford gates in the Ising-anyon topological quantum computer
• Topologically protected quantum gates for computation with non-Abelian anyons in the Pfaffian quantum Hall state
• Unconventional Fusion and Braiding of Topological Defects in a Lattice Model
• Towards a universal set of topologically protected gates for quantum computation with Pfaffian qubits
• Anyons from Three-Body Hard-Core Interactions in One Dimension
• Modeling electron fractionalization with unconventional Fock spaces
• Systematic construction of topological-nontopological hybrid universal quantum gates based on many-body Majorana fermion interactions
• Computational equivalence of the two inequivalent spinor representations of the braid group in the Ising topological quantum computer
• Grobner Bases for Finite-temperature Quantum Computing and their Complexity