Twist defects and projective nonAbelian braiding statistics
Abstract
It has recently been realized that a general class of nonAbelian defects can be created in conventional topological states by introducing extrinsic defects, such as lattice dislocations or superconductorferromagnet 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∝N surface. To emphasize this connection we refer to the twist defects as genons. We develop methods to compute the projective nonAbelian 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 nonAbelian braiding statistics obtained when the genons become deconfined, finiteenergy 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.
 Publication:

Physical Review B
 Pub Date:
 January 2013
 DOI:
 10.1103/PhysRevB.87.045130
 arXiv:
 arXiv:1208.4834
 Bibcode:
 2013PhRvB..87d5130B
 Keywords:

 05.30.Pr;
 73.43.f;
 03.67.Lx;
 11.15.Yc;
 Fractional statistics systems;
 Quantum Hall effects;
 Quantum computation;
 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory
 EPrint:
 26 pages, 18 Figures . v2: added references, modified universal TQC section, and other minor clarifications throughout the paper