Subsystem non-invertible symmetry operators and defects
Weiguang Cao, Linhao Li, Masahito Yamazaki, Yunqin Zheng
SciPost Phys. 15, 155 (2023) · published 12 October 2023
- doi: 10.21468/SciPostPhys.15.4.155
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Abstract
We explore non-invertible symmetries in two-dimensional lattice models with subsystem $\mathbb Z_2$ symmetry. We introduce a subsystem $\mathbb Z_2$-gauging procedure, called the subsystem Kramers-Wannier transformation, which generalizes the ordinary Kramers-Wannier transformation. The corresponding duality operators and defects are constructed by gaugings on the whole or half of the Hilbert space. By gauging twice, we derive fusion rules of duality operators and defects, which enriches ordinary Ising fusion rules with subsystem features. Subsystem Kramers-Wannier duality defects are mobile in both spatial directions, unlike the defects of invertible subsystem symmetries. We finally comment on the anomaly of the subsystem Kramers-Wannier duality symmetry, and discuss its subtleties.
Cited by 6
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 2 Weiguang Cao,
- 1 3 Linhao Li,
- 1 2 Masahito Yamazaki,
- 2 3 Yunqin Zheng
- 1 東京大学 / University of Tokyo [UT]
- 2 Kavli Institute for the Physics and Mathematics of the Universe [IPMU]
- 3 Institute for Solid State Physics, University of Tokyo [ISSP]