Topological quasiparticles and the holographic bulkedge relation in (2+1)dimensional stringnet models
Abstract
Stringnet models allow us to systematically construct and classify (2+1)dimensional [(2+1)D] topologically ordered states which can have gapped boundaries. We can use a simple ideal stringnet wave function, which is described by a set of Fmatrices [or more precisely, a unitary fusion category (UFC)], to study all the universal properties of such a topological order. In this paper, we describe a finite computational method, Qalgebra approach, that allows us to compute the nonAbelian statistics of the topological excitations [or more precisely, the unitary modular tensor category (UMTC)], from the stringnet wave function (or the UFC). We discuss several examples, including the topological phases described by twisted gauge theory [i.e., twisted quantum double D^{α}(G)]. Our result can also be viewed from an angle of holographic bulkboundary relation. The (1+1)dimensional [(1+1)D] anomalous topological orders, that can appear as edges of (2+1)D topological states, are classified by UFCs which describe the fusion of quasiparticles in (1+1)D. The (1+1)D anomalous edge topological order uniquely determines the (2+1)D bulk topological order (which are classified by UMTC). Our method allows us to compute this bulk topological order (i.e., the UMTC) from the anomalous edge topological order (i.e., the UFC).
 Publication:

Physical Review B
 Pub Date:
 September 2014
 DOI:
 10.1103/PhysRevB.90.115119
 arXiv:
 arXiv:1311.1784
 Bibcode:
 2014PhRvB..90k5119L
 Keywords:

 71.10.w;
 02.20.Uw;
 03.65.Fd;
 Theories and models of manyelectron systems;
 Quantum groups;
 Algebraic methods;
 Condensed Matter  Strongly Correlated Electrons;
 Mathematics  Category Theory;
 Mathematics  Quantum Algebra;
 Quantum Physics
 EPrint:
 32 pages, 8 figures, reference updated, some refinements