# Mathematics Colloquia and Seminars

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### Automorphic equivalence of gapped ground states and the classification of gapped phases

**QMAP Seminar**

Speaker: | Bruno Nachtergaele, UCDavis, Math. Dept |

Location: | 2112 MSB |

Start time: | Tue, Jan 31 2012, 12:00AM |

I will discuss the flow of automorphisms connecting ground states of model Hamiltonians belonging to the same gapped ground state phase. To illustrate how the notion of automorphic equivalence provides a useful classification of gapped ground state phases, I introduce a family of quantum spin chains with nearest neighbor interactions of which the ground states can be described as a product vacuum with a finite number of particles bound to the edges. The numbers of particles, n_L and n_R, that can bind to the left and right edges of the finite chains serve as indices of the particular phase a model belongs to. All these ground states, which we called Product Vacua with Boundary States (PVBS) can be described as Matrix Product States (MPS). As an example I present a curve of Hamiltonians connecting the AKLT model to its representative PVBS model, which has indices n_L=n_R=1. (joint work with Sven Bachmann, Spyridon Michalakis, and Robert Sims)