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

Minyoung You

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arXiv · 2609.32266

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 $\mathrm{Rep}(D_8)$ SPT phases, may not be connected by any symmetric entangler. We show that the three $\mathrm{Rep}(D_8)$ 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 $\mathrm{Rep}(D_8)$ SPT phases, and show that its action on string order parameters reproduces the anyon permutation predicted by the TQFT duality.

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Minyoung You. 2026-09-26. Symmetry-permuting entanglers for non-invertible symmetry-protected topological phases. https://arxiv.org/abs/2609.32266

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