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arXiv · 2406.05454

Generating Lattice Non-invertible Symmetries

Weiguang Cao·Linhao Li·Masahito Yamazaki
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Abstract

Lattice non-invertible symmetries have rich fusion structures and play important roles in understanding various exotic topological phases. In this paper, we explore methods to generate new lattice non-invertible transformations/symmetries from a given non-invertible seed transformation/symmetry. The new lattice non-invertible symmetry is constructed by composing the seed transformations on different sites or sandwiching a unitary transformation between the transformations on the same sites. In addition to known non-invertible symmetries with fusion algebras of Tambara-Yamagami $\mathbb Z_N\times\mathbb Z_N$ type, we obtain a new non-invertible symmetry in models with $\mathbb Z_N$ dipole symmetries. We name the latter the dipole Kramers-Wannier symmetry because it arises from gauging the dipole symmetry. We further study the dipole Kramers-Wannier symmetry in depth, including its topological defect, its anomaly and its associated generalized Kennedy-Tasaki transformation.

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Weiguang Cao, Linhao Li, Masahito Yamazaki. 2024-06-08. Generating Lattice Non-invertible Symmetries. https://doi.org/10.21468/scipostphys.17.4.104

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