Special Physics Theory Seminar with Clement Delcamp on Two-Dimensional Spin Systems

I will present a framework to systematically investigate so-called higher categorical symmetries in two-dimensional spin systems. Though exotic, such generalised symmetries have been shown to naturally arise as dual symmetries upon gauging invertible symmetries. Given an arbitrary two-dimensional spin system with an ordinary symmetry, I will explain how to perform the (twisted) gauging of any of its sub-symmetries and demonstrate that the resulting model has a symmetry structure encoded into a fusion 2-category. I will exemplify this approach by specialising to certain finite group generalisations of the transverse-field Ising model, for which we can explicitly define lattice symmetry operators organised into fusion 2-categories of higher representations of higher groups.