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PreprintCC BY 4.0arXiv

Symmetry-permuting entanglers for non-invertible symmetry-protected topological phases

  • Minyoung You
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Abstract

1+1D symmetry-protected topological (SPT) phases with invertible symmetry can be characterized by the symmetric entanglers: globally symmetric finite-depth local unitary circuits that generate representative ground states from a product state. For non-invertible symmetries, however, distinct SPT phases, such as the three Rep(D8) SPT phases, may not be connected by any symmetric entangler. We show that the three Rep(D8) SPT phases can nevertheless be connected by \emph{symmetry-permuting} finite-depth local unitary circuits, realizing dualities predicted by topological quantum field theory (TQFT). We construct an explicit matrix product unitary connecting two of the Rep(D8) SPT phases, and show that its action on string order parameters reproduces the anyon permutation predicted by the TQFT duality.

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Cite

BibTeXRIS
BibTeX
@misc{you2026symmetrypermuting,
  title = {{Symmetry-permuting entanglers for non-invertible symmetry-protected topological phases}},
  author = {Minyoung You},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.32266},
  eprint = {2609.32266},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.32266},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Symmetry-permuting entanglers for non-invertible symmetry-protected topological phases
AU  - Minyoung You
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.32266
UR  - https://arxiv.org/abs/2609.32266
AB  - 1+1D symmetry-protected topological (SPT) phases with invertible symmetry can be characterized by the symmetric entanglers: globally symmetric finite-depth local unitary circuits that generate representative ground states from a product state. For non-invertible symmetries, however, distinct SPT phases, such as the three Rep(D_8) SPT phases, may not be connected by any symmetric entangler. We show that the three Rep(D_8) SPT phases can nevertheless be connected by \emph{symmetry-permuting} finite-depth local unitary circuits, realizing dualities predicted by topological quantum field theory (TQFT). We construct an explicit matrix product unitary connecting two of the Rep(D_8) SPT phases, and show that its action on string order parameters reproduces the anyon permutation predicted by the TQFT duality.
ER  -