Jean-Noël Fuchs: Topological order in two dimensions in toy models

par Jean-Noël Fuchs

vendredi 17 oct. 2025, 09:30 → 12:00 Europe/Paris

M7-411 (ENS Lyon)

In this talk, I will discuss the notion of topological order and anyons in two dimensions. I will contrast topological order with the different notion of topological insulator and topological bands. In a first introductory part, I will concentrate on the situation at zero temperature and detail the "Ising model of topological order", i.e. the toric code. Then in a second part, I will discuss the recent work that we did during the PhD of Anna Ritz-Zwilling on topological order at finite temperature studying several toy models: the string nets of Levin and Wen and the Kitaev quantum double. For all these models, we find that topological order is destroyed at finite temperature in the thermodynamic limit. However, in a finite-size system, there is a finite temperature below which topological order is preserved.