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arXiv · 2504.20151

$N$-ality symmetry and SPT phases in (1+1)d

Jun Maeda·Tsubasa Oishi
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Abstract

Duality symmetries have been extensively investigated in various contexts, playing a crucial role in understanding quantum field theory and condensed matter theory. In this paper, we extend this framework by studying $N$-ality symmetries, which are a generalization of duality symmetries and are mathematically described by $\mathbb{Z}_N$-graded fusion categories. In particular, we focus on an $N$-ality symmetry obtained by gauging a non-anomalous subgroup of $\mathbb{Z}_N\times\mathbb{Z}_N\times\mathbb{Z}_N$ symmetry with a type III anomaly. We determine the corresponding fusion rules via two complementary approaches: a direct calculation and a representation-theoretic method. As an application, we study the symmetry-protected topological (SPT) phases associated with the $N$-ality symmetry. We classify all such SPT phases using the SymTFT framework and explicitly construct lattice Hamiltonians for some of them.

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Jun Maeda, Tsubasa Oishi. 2025-04-28. $N$-ality symmetry and SPT phases in (1+1)d. https://doi.org/10.1007/jhep12(2025)063

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