Cluster State as a Noninvertible Symmetry-Protected Topological Phase,Physical Review Letters

当前位置： X-MOL 学术 › Phys. Rev. Lett. › 论文详情

Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)

Cluster State as a Noninvertible Symmetry-Protected Topological Phase
Physical Review Letters ( IF 8.1 ) Pub Date : 2024-09-10 , DOI: 10.1103/physrevlett.133.116601
Sahand Seifnashri ₁ , Shu-Heng Shao ₂

Affiliation

We show that the standard

1 + 1 D

Z_{2} \times Z_{2}

cluster model has a noninvertible global symmetry, described by the fusion category

Rep (D_{8})

. Therefore, the cluster state is not only a

Z_{2} \times Z_{2}

symmetry protected topological (SPT) phase, but also a noninvertible 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 noninvertible SPT phases. Finally, we show that there does not exist a symmetric entangler that maps between these distinct SPT states.

中文翻译：