1+1d SPT phases with fusion category symmetry: interface modes and non-abelian Thouless pump

• URL: http://arxiv.org/abs/2408.15960v1
• Date: Wed, 28 Aug 2024 17:26:18 GMT
• Title: 1+1d SPT phases with fusion category symmetry: interface modes and non-abelian Thouless pump
• Authors: Kansei Inamura, Shuhei Ohyama,
• Abstract summary: We consider $mathcalC$-SPT phases with finite non-invertible symmetry in 1+1d. We show that there must be a degenerate interface mode between different $mathcalC$-SPT phases. Our invariant is identified with a non-abelian generalization of the Thouless charge pump.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider symmetry protected topological (SPT) phases with finite non-invertible symmetry $\mathcal{C}$ in 1+1d. In particular, we investigate interfaces and parameterized families of them within the framework of matrix product states. After revealing how to extract the $\mathcal{C}$-SPT invariant, we identify the algebraic structure of symmetry operators acting on the interface of two $\mathcal{C}$-SPT phases. By studying the representation theory of this algebra, we show that there must be a degenerate interface mode between different $\mathcal{C}$-SPT phases. This result generalizes the bulk-boundary correspondence for ordinary SPT phases. We then propose the classification of one-parameter families of $\mathcal{C}$-SPT states based on the explicit construction of invariants of such families. Our invariant is identified with a non-abelian generalization of the Thouless charge pump, which is the pump of a local excitation within a $\mathcal{C}$-SPT phase. Finally, by generalizing the results for one-parameter families of SPT phases, we conjecture the classification of general parameterized families of general gapped phases with finite non-invertible symmetries in both 1+1d and higher dimensions.

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