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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 13: Gitterfeldtheorie 2

MP 13.3: Vortrag

Donnerstag, 28. Februar 2013, 15:35–16:00, HS 8

Elementary (quasi)particles with braided statistics — •Pieter Naaijkens — Leibniz Universität Hannover, Deutschland

Quantum mechanical systems with (quasi)particles or excitations that have braided (or anyonic) statistics (as opposed to the usual Bose/Fermi alternative) have received a lot of attention in recent years. Such (quasi)particles are also called anyons. In this talk we will discuss how these excitations and their properties can be obtained from first priciples. The focus will be on models defined on a plane, for example Kitaev’s toric code. The latter can be interpreted as a lattice gauge theory with local Z₂ × Z₂ gauge symmetry. Starting from the algebra of observables of this model, given in a ground state representation, all properties of the anyons in this system (such as braiding and fusion) can be recovered. The results match with one expects from known properties of the model when defined on a torus.

We will also comment on recent work, relating the number of equivalence classes of such (quasi)particles to the Kosaki-Longo (or Jones) index of certain inclusions of observable algebras.