Weak Hopf symmetry behind the 2d topological phases
Organizers
Speaker
Zhian Jia
Time
Tuesday, April 2, 2024 5:00 PM - 6:00 PM
Venue
A3-3-301
Online
Zoom 242 742 6089
(BIMSA)
Abstract
Two-dimensional (2d) topological phases are characterized by a unitary modular tensor category (UMTC) along with the chiral central charge $c_{-}$. For non-chiral topological phases, where $c_{-}$ vanishes, the topological phase is fully described by a UMTC. There are two prominent classes of lattice models that realize 2d non-chiral topological phases: (i) Kitaev’s quantum double models and (ii) Levin and Wen’s string-net models. These two model classes are intimately related. This talk will present a generalization of Kitaev’s quantum double models to weak Hopf algebras, as well as a generalization of Levin-Wen string-net models to multifusion categories. We will establish an equivalence between these two broader classes of lattice models for non-chiral 2D topological phases. From the perspective of lattice gauge theory, we introduce weak Hopf gauge and charge symmetries. In particular, we elucidate the weak Hopf symmetry underlying the multifusion string-net models. Some interesting open problems related to these generalizations will also be highlighted.