SIMIS Seminar on Field Theory and String Theory: Non-invertible Symmetry in Lattice Models

Speaker: Weiguang Cao (IPMU, Tokyo University)

Abstract: Recently, the notion of symmetry has been generalized. While ordinary symmetry can be described by a (1) co-dimension 1, (2) topological operator with (3) group-like fusion rule, generalized symmetries are described by operators that relax one or more conditions. Generalized symmetry plays an important role not only in constraining the low energy dynamics but also in classifying exotic phases of matter. In my talk, I will focus on non-invertible symmetry, which satisfies a more general fusion rule, in lattice models with exotic symmetries that are not topological in the spatial direction. These exotic symmetries appear in fracton models where quasiparticles with restricted mobility are allowed. I will first review the construction of Kramers-Wannier duality operators and defects in the transverse Ising model and show their non-invertible property. Then, I will generalize the method to lattice models with subsystem symmetry to show that non-invertible symmetry appears also in these models with exotic symmetries. I will also discuss about the anomaly of the noninvertible symmetry.

Time: 16:00 ~ 17:00, Tue., Apr. 9, 2024

Location: Floor 6, Innovation Center Building 3, Weicheng Road 62, Yangpu District, Shanghai, China

Zoom Meeting No.: 423 317 8953
Password: SIMIS

Organizer: Sen Hu, Andrey Losev, Bong Lian, Wen-Jie Ma, Hao Zou

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