"Fock Parafermions and SelfDual Representations of the Braid Group"Emilio Cobanera , Leiden University [Host: Israel Klich]
ABSTRACT:
Because of potential relevance to topological quantum information processing, we introduce and study the selfdual family of representations of the braid group. Selfdual representations are physically motivated by strongcoupling/weakcoupling dualities in clock models and include as special cases the Majorana and Gaussian (metaplectic) representations. To show that selfdual representations admit a particle interpretation, we introduce and describe in second quantization a family of particle species with (p=2,3,dots) exclusion and ( heta=2pi/p) exchange statistics. We call these anyons Fock parafermions, because they are the particles naturally associated to the parafermionic zeroenergy modes potentially realizable in mesoscopic arrays of fractional topological insulators. Selfdual representations are local combinations of either parafermions or Fock parafermions, an important requisite for the potential physical implementation of (semi)topologically protected quantum logic gates. The secondquantization description of Fock parafermions entails the concept of Fock algebra, i.e., a Fock space endowed with a statistical multiplication that captures and logically correlates these anyons' exclusion and exchange statistics. As a consequence, normalordering remains a welldefined operation.

Condensed Matter Seminar Thursday, August 15, 2013 3:30 PM Physics Building, Room 204 Note special room. 
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