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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 3: Quanten-Information III

MP 3.6: Vortrag

Dienstag, 18. März 2014, 12:10–12:30, SPA SR125

Haag Duality in Kitaev's Quantum Double Model for Finite Groups — •Leander Fiedler and Pieter Naaijkens — Institut für Theoretische Physik, Leibniz Universität Hannover, Germany

Kitaev's quantum double model for finite groups is a spin model on a 2D lattice that exhibits anyonic excitations. It is designed to perform quantum computations and in fact for certain groups it allows even for universal quantum computation. The latter is made possible by braid statistics of the anyons which are encoded in the superselection structure of the model.

We show that algebras of observables localized in cone-like regions fulfill Haag duality in the vacuum representation. This means that in the vacuum representation observables which commute with all observables outside the cone are exactly those localized inside the cone.

As an application we consider an analysis of the superselection structure of the model for finite abelian groups. We show that in this case the superselection structure is given by conelike localized endomorphisms describing single excitations of the model. The latter can be described by representations of Drinfeld's quantum double of the underlying group. This resembles analogue results for Kitaev's toric code model.