Regensburg 2010 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 41: CE: Low-dimensional Systems - Models 2

TT 41.5: Vortrag

Freitag, 26. März 2010, 11:30–11:45, H21

Breakdown of the topologically-ordered Z(3) Toric Code — •Marc Daniel Schulz¹, Sébastien Dusuel², Julien Vidal³, and Kai Phillip Schmidt¹ — ¹Lehrstuhl für Theoretische Physik I, Otto-Hahn-Strasse 4, TU Dortmund, 44221 Dortmund, Germany — ²Lycée Saint-Louis, 44 Boulevard Saint-Michel, 75006 Paris, France — ³Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France

The standard Toric Code invented by Kitaev is an exactly solvable two-dimensional spin 1/2 model which exhibits an topologically ordered ground state and is strongly debated in the context of topological quantum computation. The elementary excitations are Z(2) Abelian anyons which are completely local because they are protected by conservation laws. Here we investigate an extension of the Toric Code to Z(3) anyons which yields a higher degeneracy of the groundstate and is thus a more favorable candidate towards a realization of a topological quantum memory. Our major aim is to understand the breakdown of a topologically ordered state with Z(3) anyonic excitations. To this end we study the influence of an external ’magnetic field’ which leads to dynamic and interacting Z(3) anyons. As a consequence, one expects a rich phase diagram with interesting phase transitions out of the topological phase. We use perturbative continous unitary transformations to derive an effective low-energy describtion for the relevant elementary excitations in order to study this question.