Affiliation:
1. Kavli Institute for the Physics and Mathematics of the Universe
2. University of Tokyo
3. Institute for Solid State Physics, University of Tokyo
Abstract
We explore non-invertible symmetries in two-dimensional lattice models with subsystem \mathbb Z_2ℤ2 symmetry. We introduce a subsystem \mathbb Z_2ℤ2-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.
Funder
Japan Science and Technology Agency
Japan Society for the Promotion of Science
Ministry of Education, Culture, Sports, Science and Technology
University of Tokyo
Subject
General Physics and Astronomy
Cited by
3 articles.
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