# Mathematics Colloquia and Seminars

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### Spectral gap stability of spin chains

**Student-Run Applied & Math Seminar**

Speaker: | Alvin Moon |

Location: | 2112 MSB |

Start time: | Wed, Apr 19 2017, 12:10PM |

A stable spectral gap in a quantum spin system (QSS) guarantees the persistence of many important properties of the quantum system through relatively small perturbations. Using techniques such as quasi-adiabatic evolution, also known as spectral flow, and Lieb-Robinson bounds, recent works have rigorously established spectral gap stability for a large class of QSS.

In this talk, we will introduce QSS as C*-dynamical systems. Then we will explain the latest results for interactions defined on lattices with periodic boundary conditions and satisfying local topological quantum order. To conclude, we will demonstrate an extension of stability to a class of one dimensional systems with open boundaries, a class containing the Affleck-Kennedy-Lieb-Tasaki spin S=1 chain.

Register for pizza here.