Global symmetries of quantum lattice models under non-invertible dualities

Cao, Weiguang; Miao, Yuan; Yamazaki, Masahito

doi:10.21468/SciPostPhysCore.8.4.070

SciPost Physics Core

Global symmetries of quantum lattice models under non-invertible dualities

Weiguang Cao, Yuan Miao, Masahito Yamazaki

SciPost Phys. Core 8, 070 (2025) · published 14 October 2025

doi: 10.21468/SciPostPhysCore.8.4.070
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Abstract

Non-invertible dualities/symmetries have become an important tool in the study of quantum field theories and quantum lattice models in recent years. One of the most studied examples is non-invertible dualities obtained by gauging a discrete group. When the physical system has more global symmetries than the gauged symmetry, it has not been thoroughly investigated how those global symmetries transform under non-invertible duality. In this paper, we study the change of global symmetries under non-invertible duality of gauging a discrete group $G$ in the context of (1+1)-dimensional quantum lattice models. We obtain the global symmetries of the dual model by focusing on different Hilbert space sectors determined by the $\mathrm{Rep}(G)$ symmetry. We provide general conjectures of global symmetries of the dual model forming an algebraic ring of the double cosets. We present concrete examples of the XXZ models and the duals, providing strong evidence for the conjectures.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.8.4.070
TI  - Global symmetries of quantum lattice models under non-invertible dualities
PY  - 2025/10/14
UR  - https://www.scipost.org/SciPostPhysCore.8.4.070
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 8
IS  - 4
SP  - 070
A1  - Cao, Weiguang
AU  - Miao, Yuan
AU  - Yamazaki, Masahito
AB  - Non-invertible dualities/symmetries have become an important tool in the study of quantum field theories and quantum lattice models in recent years. One of the most studied examples is non-invertible dualities obtained by gauging a discrete group. When the physical system has more global symmetries than the gauged symmetry, it has not been thoroughly investigated how those global symmetries transform under non-invertible duality. In this paper, we study the change of global symmetries under non-invertible duality of gauging a discrete group $G$ in the context of (1+1)-dimensional quantum lattice models. We obtain the global symmetries of the dual model by focusing on different Hilbert space sectors determined by the $\mathrm{Rep}(G)$ symmetry. We provide general conjectures of global symmetries of the dual model forming an algebraic ring of the double cosets. We present concrete examples of the XXZ models and the duals, providing strong evidence for the conjectures.
ER  -

@Article{10.21468/SciPostPhysCore.8.4.070,
	title={{Global symmetries of quantum lattice models under non-invertible dualities}},
	author={Weiguang Cao and Yuan Miao and Masahito Yamazaki},
	journal={SciPost Phys. Core},
	volume={8},
	pages={070},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.8.4.070},
	url={https://scipost.org/10.21468/SciPostPhysCore.8.4.070},
}

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