Cluster state as a noninvertible SPT phase

CMSA EVENTS: CMSA QUANTUM MATTER IN MATH & PHYSICS SEMINAR

When: March 13, 2024
11:00 am - 12:30 pm
Where: CMSA, 20 Garden St, G10
Address: 20 Garden Street, Cambridge, MA 02138, United States
Speaker: Shu-Heng Shao - SUNY Stony Brook
We will point out a non-invertible symmetry of the ordinary 1+1d Z2xZ2 cluster Hamiltonian. Therefore, the cluster state can be viewed as a non-invertible SPT phase under this fusion category symmetry, which is Rep(D8). We furthermore find two new stabilizer states that are distinct from the cluster state as Rep(D8) SPT phases, but identical as Z2xZ2 SPT phases. Finally, we discuss the degenerate edge modes at the interfaces between these three Rep(D8) SPT phases.
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