Symmetry Topological Order correspondence and Generalized Symmetries

by Oemer Aksoy

Tuesday 12 May 2026, 11:00 → 12:00 Europe/Zurich

Teams

Symmetry is one of the most powerful tools in physics. On the one hand, the presence of symmetries can constraint the spectral properties in the form of conservation laws or anomalies. On the other hand, the phases of matter can be characterized and organized by their corresponding (spontaneous) symmetry breaking patterns. Recently a deep connection between the symmetry structure of quantum matter in d-dimensional space and topological orders in (d+1)-dimensional space, the so-called symmetry-topological-order (SymTO) correspondence, has been uncovered. In this talk, I will give a pedagogical review of the SymTO construction for the simplest paradigmatic examples of spontaneous symmetry breaking and topological orders, namely the transverse field Ising model in one-dimensional space and Kitaev's toric code in two-dimensional space, respectively. I will then show how SymTO framework can be used to organize the phases of matter realized in quantum spin chains with non-invertible symmetries i.e., unusual symmetry transformations that do not have an inverse and, hence, are not implemented by unitary operators. No prior knowledge on topological orders or SymTO correspondence is needed.