TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.4.104
TI  - Generating lattice non-invertible symmetries
PY  - 2024/10/04
UR  - https://scipost.org/SciPostPhys.17.4.104
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 4
SP  - 104
A1  - Cao, Weiguang
AU  - Li, Linhao
AU  - Yamazaki, Masahito
AB  - 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 $\mathbb Z_N×\mathbb Z_N$ 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.
ER  -

@Article{10.21468/SciPostPhys.17.4.104,
	title={{Generating lattice non-invertible symmetries}},
	author={Weiguang Cao and Linhao Li and Masahito Yamazaki},
	journal={SciPost Phys.},
	volume={17},
	pages={104},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.4.104},
	url={https://scipost.org/10.21468/SciPostPhys.17.4.104},
}