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Intrinsically/Purely Gapless-SPT from Non-Invertible Duality Transformations

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arxiv 2307.04788 v1 pith:KZBY4GPD submitted 2023-07-10 cond-mat.str-el hep-th

Linhao Li , Masaki Oshikawa , Yunqin Zheng This is my paper · ORCID
classification cond-mat.str-elhep-th
keywords gaplessconstructconstructiongappedintrinsicallysymmetrytopologicaltransformation
verification ladder T0 review T1 audit T2 compute T3 formal
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The Kennedy-Tasaki (KT) transformation was used to construct the gapped symmetry protected topological (SPT) phase from the symmetry breaking phase with open boundary condition, and was generalized in our proceeding work [L. Li et al. arXiv:2301.07899] on a ring by sacrificing the unitarity, and should be understood as a non-invertible duality transformation. In this work, we further apply the KT transformation to systematically construct gapless symmetry protected topological phases. This construction reproduces the known examples of (intrinsically) gapless SPT where the non-trivial topological features come from the gapped sectors by means of decorated defect constructions. We also construct new (intrinsically) purely gapless SPTs where there are no gapped sectors, hence are beyond the decorated defect construction. This construction elucidates the field theory description of the various gapless SPTs, and can also be applied to analytically study the stability of various gapless SPT models on the lattice under certain symmetric perturbations.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Distinct finite-temperature phase diagrams of non-invertible Kennedy--Tasaki duals

    cond-mat.str-el 2026-07 accept novelty 7.0 of 10

    In three dimensions, a cluster-model interpolation and its non-invertible Kennedy–Tasaki dual have inequivalent finite-T phase diagrams over a finite window of the interpolation, proven exactly at s=0 and mapped by QMC.

  2. Symmetry theta angles and topological Witten effects

    hep-th 2025-06 conditional novelty 7.0 of 10

    Symmetry theta angles are intrinsic, Lagrangian-independent parameters of any non-anomalous Abelian invertible symmetry, and their universal effect is a topological Witten effect that shuffles twisted sectors while pr...

  3. Notes on (-2)-form symmetries

    hep-th 2026-06 unverdicted novelty 6.0 of 10

    Introduces (-2)-form symmetries that modify the SymTFT action to relate QFTs differing by anomaly data or non-invertible symmetry associators, illustrated in 2D-4D models, fusion categories, club-sandwich RG flows, an...

  4. SymTFT actions, Condensable algebras and Categorical anomaly resolutions

    hep-th 2025-09 conditional novelty 6.0 of 10

    For Q8 and Rep(Q8), the paper computes condensable algebras, identifies intrinsically gapless SPT phases, and derives fusion-category short exact sequences that resolve categorical anomalies.

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