Duality viewpoint of criticality
- URL: http://arxiv.org/abs/2209.13450v4
- Date: Fri, 6 Jan 2023 05:06:52 GMT
- Title: Duality viewpoint of criticality
- Authors: Linhao Li, Yuan Yao
- Abstract summary: We study quantum many-body systems which are self-dual under duality transformation connecting different symmetry protected topological phases.
We provide a geometric explanation of the criticality of these self-dual models.
We illustrate our results with several examples in one and two dimensions, which separate two different SPTs.
- Score: 10.697358928025304
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this work, we study quantum many-body systems which are self-dual under
duality transformation connecting different symmetry protected topological
(SPT) phases. We provide a geometric explanation of the criticality of these
self-dual models. More precisely, we show a ground state (quasi-)degeneracy
under the periodic boundary conditions,i.e., the ingappability of the bulk
spectrum. Equivalently, the symmetry group at criticality, including the
duality symmetry, has a mixed 't Hooft anomaly. This approach can not only
predict the spectrum of the self-dual model with ordinary 0-form symmetry, but
also be applied to that with generalized symmetry, such as higher form and
subsystem symmetry. As an application, we illustrate our results with several
examples in one and two dimensions, which separate two different SPTs.
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