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Qiuzhen College, Tsinghua University
Yau Mathematical Sciences Center, Tsinghua University (YMSC)
Tsinghua Sanya International  Mathematics Forum (TSIMF)
Shanghai Institute for Mathematics and  Interdisciplinary Sciences (SIMIS)
BIMSA > BIMSA TQFT and Higher Symmetries Seminar The curious symmetry breaking of SO(n) AKLT chains
The curious symmetry breaking of SO(n) AKLT chains
Organizers
Ansi Bai , Chun Chen , Liang Kong , Yi Long Wang , Zhi Hao Zhang , Hao Zheng
Speaker
Michael Ragone
Time
Tuesday, October 22, 2024 9:30 AM - 11:30 AM
Venue
A3-1-101
Online
Zoom 482 240 1589 (BIMSA)
Abstract
We study a pair of symmetry protected topological (SPT) phases which arise when considering one-dimensional quantum spin systems possessing a natural orthogonal group symmetry, the so-called O(n) chains. Particular attention is given to a family of exactly solvable models whose ground states admit a matrix product state description and generalize the AKLT chain. We call these models “SO(n) AKLT chains” and the phase they occupy the “SO(n) Haldane phase”. We discuss their ground state structure and, when n is even, their peculiar O(n)-to-SO(n) symmetry breaking. We extend a definition of Ogata’s of an SPT index for a split state for a finite symmetry group G to an SPT index for a compact Lie group G. We then compute this index, which takes values in the second Borel group cohomology H2(SO(n),U(1)), at a single point in each of the SPT phases. The two points have different indices, confirming the two SPT phases are indeed distinct. Joint work with Bruno Nachtergaele https://arxiv.org/pdf/2403.09951 .
Beijing Institute of Mathematical Sciences and Applications
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