$N$-ality symmetry and SPT phases in (1+1)d
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911315066355712 |
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| author | Maeda, Jun Oishi, Tsubasa |
| author_facet | Maeda, Jun Oishi, Tsubasa |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20151 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $N$-ality symmetry and SPT phases in (1+1)d Maeda, Jun Oishi, Tsubasa High Energy Physics - Theory Strongly Correlated Electrons 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. |
| title | $N$-ality symmetry and SPT phases in (1+1)d |
| topic | High Energy Physics - Theory Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2504.20151 |