# Mathematics Colloquia and Seminars

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### Anyons in topologically ordered phases

**Student-Run Applied & Math Seminar**

Speaker: | Matthew Cha |

Location: | 2112 MSB |

Start time: | Fri, Apr 24 2015, 12:10PM |

The ground state of a many-body quantum system can be topologically ordered. This may be manifested through ground state degeneracy on surfaces of different genus, long range entanglement within the ground state, and, in two dimensions, quasi-particle excitations which have braided statistic. Working in the framework of quantum spin systems, I will introduce the notion of a gapped ground state phase and discuss the role of topological order in the stability of ground state phases. I then consider certain Hamiltonian lattice models which have quasi-particle excitations with braid statistics, these are called anyons. We discuss how one can use the theory of superselection sectors to analyze particle type, braiding and stability.