Gauging non-invertible symmetries on the lattice

Seifnashri, Sahand; Shao, Shu-Heng; Yang, Xinping

doi:10.21468/SciPostPhys.19.2.063

SciPost Physics

Gauging non-invertible symmetries on the lattice

Sahand Seifnashri, Shu-Heng Shao, Xinping Yang

SciPost Phys. 19, 063 (2025) · published 29 August 2025

doi: 10.21468/SciPostPhys.19.2.063
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Abstract

We provide a general prescription for gauging finite non-invertible symmetries in 1+1d lattice Hamiltonian systems. Our primary example is the Rep(D$_8$) fusion category generated by the Kennedy-Tasaki transformation, which is the simplest anomaly-free non-invertible symmetry on a spin chain of qubits. We explicitly compute its lattice F-symbols and illustrate our prescription for a particular (non-maximal) gauging of this symmetry. In our gauging procedure, we introduce two qubits around each link, playing the role of "gauge fields" for the non-invertible symmetry, and impose novel Gauss's laws. Similar to the Kramers-Wannier transformation for gauging an ordinary $\mathbb{Z}_2$, our gauging can be summarized by a gauging map, which is part of a larger, continuous non-invertible cosine symmetry.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.19.2.063
TI  - Gauging non-invertible symmetries on the lattice
PY  - 2025/08/29
UR  - https://www.scipost.org/SciPostPhys.19.2.063
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 19
IS  - 2
SP  - 063
A1  - Seifnashri, Sahand
AU  - Shao, Shu-Heng
AU  - Yang, Xinping
AB  - We provide a general prescription for gauging finite non-invertible symmetries in 1+1d lattice Hamiltonian systems. Our primary example is the Rep(D$_8$) fusion category generated by the Kennedy-Tasaki transformation, which is the simplest anomaly-free non-invertible symmetry on a spin chain of qubits. We explicitly compute its lattice F-symbols and illustrate our prescription for a particular (non-maximal) gauging of this symmetry. In our gauging procedure, we introduce two qubits around each link, playing the role of "gauge fields" for the non-invertible symmetry, and impose novel Gauss's laws. Similar to the Kramers-Wannier transformation for gauging an ordinary $\mathbb{Z}_2$, our gauging can be summarized by a gauging map, which is part of a larger, continuous non-invertible cosine symmetry.
ER  -

@Article{10.21468/SciPostPhys.19.2.063,
	title={{Gauging non-invertible symmetries on the lattice}},
	author={Sahand Seifnashri and Shu-Heng Shao and Xinping Yang},
	journal={SciPost Phys.},
	volume={19},
	pages={063},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.19.2.063},
	url={https://scipost.org/10.21468/SciPostPhys.19.2.063},
}

Cited by 3

Ontology / Topics

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Anomalies Discrete gauge theories Global symmetries Quantum spin chains

Authors / Affiliations: mappings to Contributors and Organizations

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¹ Sahand Seifnashri,
² ³ Shu-Heng Shao,
⁴ Xinping Yang

Funders for the research work leading to this publication