Topological order: Anyons and Fractons

1-12 Apr 2024 Les Houches (France)

Aims

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.

Topics and lecturers

First week (2-6 April):

Symmetry protected topological order and fracton order : Xie Chen (Caltech, USA) 6h

Introduction to fusion categories: Benoît Douçot (CNRS & Sorbonne University, France) 2h

Quantum Hall states and topological insulators : Kareljan Schoutens (University of Amsterdam, NL) 6h

Topological order and anyons : Steve Simon (Oxford University, UK) 6h

Anyon condensation : Joost Slingerland (Maynooth University, Ireland) 2h

Second week (8-12 April):

Engineering topological many-body phases with cold atoms: Monika Aidelsburger (LMU Munich, Germany) 2h

Topological superconductivity and Majorana zero modes : Carlo Beenakker (Leiden University, NL) 2h

Topological quantum computation and quantum error correction: Benjamin Brown (IBM Quantum, Denmark) 2h

(3+1)d topological order: Clément Delcamp (IHES, France) 2h

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

Quantum spin liquids and frustrated magnets : Grégoire Misguich (CEA Saclay, France) 2h

Quantum groups and dualities: Vincent Pasquier (CEA Saclay, France) 2h

Basics of tensor network states: Antoine Tilloy (INRIA, Paris, France) 2h

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