Cluster state as a non-invertible symmetry protected topological phase

• URL: http://arxiv.org/abs/2404.01369v2
• Date: Thu, 26 Sep 2024 02:56:16 GMT
• Title: Cluster state as a non-invertible symmetry protected topological phase
• Authors: Sahand Seifnashri, Shu-Heng Shao,
• Abstract summary: We show that the standard 1+1d $mathbbZ tensortimes mathbbZ$ cluster model has a non-invertible global symmetry. We identify the edge modes and the local projective algebras at the interfaces between these non-invertible SPT phases.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We show that the standard 1+1d $\mathbb{Z}_2\times \mathbb{Z}_2$ cluster model has a non-invertible global symmetry, described by the fusion category Rep(D$_8$). Therefore, the cluster state is not only a $\mathbb{Z}_2\times \mathbb{Z}_2$ symmetry protected topological (SPT) phase, but also a non-invertible SPT phase. We further find two new commuting Pauli Hamiltonians for the other two Rep(D$_8$) SPT phases on a tensor product Hilbert space of qubits, matching the classification in field theory and mathematics. We identify the edge modes and the local projective algebras at the interfaces between these non-invertible SPT phases. Finally, we show that there does not exist a symmetric entangler that maps between these distinct SPT states.

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