{"title":"1+1d SPT phases with fusion category symmetry: interface modes and non-abelian Thouless pump","authors":"Kansei Inamura, Shuhei Ohyama","doi":"arxiv-2408.15960","DOIUrl":null,"url":null,"abstract":"We consider symmetry protected topological (SPT) phases with finite\nnon-invertible symmetry $\\mathcal{C}$ in 1+1d. In particular, we investigate\ninterfaces and parameterized families of them within the framework of matrix\nproduct states. After revealing how to extract the $\\mathcal{C}$-SPT invariant,\nwe identify the algebraic structure of symmetry operators acting on the\ninterface of two $\\mathcal{C}$-SPT phases. By studying the representation\ntheory of this algebra, we show that there must be a degenerate interface mode\nbetween different $\\mathcal{C}$-SPT phases. This result generalizes the\nbulk-boundary correspondence for ordinary SPT phases. We then propose the\nclassification of one-parameter families of $\\mathcal{C}$-SPT states based on\nthe explicit construction of invariants of such families. Our invariant is\nidentified with a non-abelian generalization of the Thouless charge pump, which\nis the pump of a local excitation within a $\\mathcal{C}$-SPT phase. Finally, by\ngeneralizing the results for one-parameter families of SPT phases, we\nconjecture the classification of general parameterized families of general\ngapped phases with finite non-invertible symmetries in both 1+1d and higher\ndimensions.","PeriodicalId":501317,"journal":{"name":"arXiv - MATH - Quantum Algebra","volume":"13 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Quantum Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.15960","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 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.