Symmetric entanglers for non-invertible SPT phases

• URL: http://arxiv.org/abs/2509.04581v2
• Date: Tue, 14 Oct 2025 07:53:29 GMT
• Title: Symmetric entanglers for non-invertible SPT phases
• Authors: Minyoung You,
• Abstract summary: We argue that a symmetric entangler should exist for $1+1$d systems whenever the non-invertible symmetry has SPT phases connected by fixed-charge dualities (FCD)<n>We construct an explicit example of a symmetric entangler for the two SPT phases with $mathrmRep(A_4)$-symmetry, as a matrix product unitary (MPU)
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: It has been suggested that non-invertible symmetry protected topological phases (SPT), due to the lack of a stacking structure, do not have symmetric entanglers (globally symmetric finite-depth quantum circuits) connecting them. Using topological holography, we argue that a symmetric entangler should in fact exist for $1+1$d systems whenever the non-invertible symmetry has SPT phases connected by fixed-charge dualities (FCD). Moreover, we construct an explicit example of a symmetric entangler for the two SPT phases with $\mathrm{Rep}(A_4)$-symmetry, as a matrix product unitary (MPU).

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