Topological order was introduced by Xiao-Gang Wen in the 1990’s to explain chiral spin liquids and the fractional quantum Hall effect and as an alternative to Landau's symmetry-breaking theory of phases of matter. Two-dimensional phases with topological order have exotic excitations with anyonic exchange statistics. In 1997, Alexei Kitaev proposed topologically-protected quantum computation using anyons. It was then understood that the mathematics needed to handle topological order are that of fusion categories. In the 2010's, three-dimensional models with topological order were also proposed. Among them some have exotic excitations known as fractons. In 2021, anyonic statistics were experimentally confirmed in the fractional quantum Hall effect.
This school will take place in the famous école de physique des Houches (in the french Alps) and aims at providing a broad introduction to topological order, anyons and fractons. It will consist of a first week of mainly basic (long) lectures and a second week of more specialized (shorter) lectures. It will be mainly focused on condensed matter and quantum physics, but will also have many connections to quantum information and mathematics.
The total number of participants (including the speakers and organizers) will be between 55 and 70. All participants are expected to present a poster. There will be a flash presentation to advertise the posters at the beginnning of the school.
Format
3 basic lectures (6 hours each).
12 specialized lectures on advanced topics (2 hours each).
2 poster sessions and correspondingly 2 oral flash presentations of the posters.
Topics and lecturers
First week (2-6 April):
Symmetry protected topological order and fracton order : Xie Chen (Caltech, USA) 6h
Matrix Product State approach to the fractional quantum Hall effect : Benoît Estienne (Sorbonne University, France) 2h
Noise measurements for the characterization of anyons in the fractional quantum Hall effect : Gwendal Fève (ENS Paris & Sorbonne University, France) 2h
Generalized symmetries and dualities: Laurens Lootens (Ghent University, Belgium) 2h