Cluster state as a non-invertible symmetry protected topological phase
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908636849111040 |
|---|---|
| author | Seifnashri, Sahand Shao, Shu-Heng |
| author_facet | Seifnashri, Sahand Shao, Shu-Heng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01369 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cluster state as a non-invertible symmetry protected topological phase Seifnashri, Sahand Shao, Shu-Heng Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics 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. |
| title | Cluster state as a non-invertible symmetry protected topological phase |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2404.01369 |