Homological codes and abelian anyons

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Homological codes and abelian anyons
2016. 04. 22. 10:15
BME Fizikai Intézet, Elméleti Fizika Tanszék, Budafoki út 8. F-épület, III lépcsőház, szemináriumi szoba
Péter Vrana (BUTE Dept. Geom.)

We study a generalization of Kitaev's abelian toric code model defined on CW complexes. In this model two-level systems are attached to n dimensional cells and the interaction is given by generalized star and plaquette operators. We find that the set of energy-minimizing ground states and the types of charges carried by certain localized excitations depends only on the proper homotopy type of the CW complex. As an application we show that the homological product of a CSS code with the infinite toric code has excitations with abelian anyonic statistics.