2023/04/19 by Weiguang Cao, Linhao Li, Masahito Yamazaki +1 · 1 voice · 2 citations
Physics and Astronomy · #cond-mat.str-el #hep-th
paper · pdf · doi:10.21468/scipostphys.15.4.155
arxiv published 2023/04/19 · arxiv updated 2023/11/02
We explore non-invertible symmetries in two-dimensional lattice models with subsystem \mathbb Z2 symmetry. We introduce a subsystem \mathbb Z2-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.