Title: Cluster states and non-invertible symmetries: a tensor network perspective

Speaker: Dr. Nathanan Tantivasadakarn, Caltech

Time: 10:00 am, May 23 (Friday), 2025

Place: Room M830, IOP-CAS (中国科学院物理研究所M830)

 

Abstract:

The one-dimensional cluster state is a paradigmatic example of a Z2xZ2 symmetry-protected topological (SPT) state in 1+1D. I will demonstrate aspects of the cluster state that makes close connections to the study of non-invertible symmetries on the lattice. First, I will show that the cluster state is deeply related to the the Kramers-Wannier duality, which realizes a non-invertible symmetry of the critical transverse-field Ising model, and how a ZX calculus, a diagrammatic presentation of linear maps between qubits from quantum information, can be used to succinctly define such non-invertible duality symmetries. Second, I will show that a generalization of the cluster state to finite groups is an example of an SPT state protected by a non-invertible symmetry, belonging to a distinct phase from the symmetric product state.

 

References:

[1] C. Fechisin, N. Tantivasadakarn, V. V. Albert, Phys. Rev. X 15, 011058 (2025).

[2] P. Gorantal, S. H. Shao, N. Tantivasadakarn, arXiv: 2406.12978.

 

About the speaker:

Nat. Tantivasadakarn obtained his Ph.D. from Harvard University and is currently a Burke postdoctoral fellow at Caltech. His research interests explore the interplay between topological phases of matter, quantum error correction and computation, non-equilibrium quantum dynamics and generalized symmetries. In this fall, he will join Stony Brook University as a new faculty member.