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Cited by 275

The DOI matches its Crossref record; 47 of the 47 references it cites were found in a registry or an index.

Twist defects and projective non-Abelian braiding statistics

Open access
Barkeshli, Maissam, Jian, Chao-Ming, Qi, Xiao-Liang·2013·Physical Review B
DOI 10.1103/physrevb.87.045130
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Abstract

It has recently been realized that a general class of non-Abelian defects can be created in conventional topological states by introducing extrinsic defects, such as lattice dislocations or superconductor-ferromagnet domain walls in conventional quantum Hall states or topological insulators. In this paper, we begin by placing these defects within the broader conceptual scheme of extrinsic twist defects associated with symmetries of the topological state. We explicitly study several classes of examples, including ${Z}_{2}$ and ${Z}_{3}$ twist defects, where the topological state with $N$ twist defects can be mapped to a topological state without twist defects on a genus $g\ensuremath{\propto}N$ surface. To emphasize this connection we refer to the twist defects as genons. We develop methods to compute the projective non-Abelian braiding statistics of the genons, and we find the braiding is given by adiabatic modular transformations, or Dehn twists, of the topological state on the effective genus $g$ surface. We study the relation between this projective braiding statistics and the ordinary non-Abelian braiding statistics obtained when the genons become deconfined, finite-energy excitations. We find that the braiding is generally different, in contrast to the Majorana case, which opens the possibility for fundamentally novel behavior. We find situations where the genons have quantum dimension 2 and can be used for universal topological quantum computing (TQC), while the host topological state is by itself nonuniversal for TQC.

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Metadata

Authors
Barkeshli, M., Jian, C.-M., & Qi, X.-L.
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
2013-01-31
Volume
87
Issue
4
ISSN
  • 1098-0121 (ISSN-L)
  • 1550-235X
DOI
10.1103/physrevb.87.045130
OpenAlex
W1808471149
Cited by
275
References
47
FWCI
15.93
Type
journal article
Language
en
Open access
green

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