Mathematical physics of anyons and topological states of matter

11 Mar 2019, 09:00 → 16 Mar 2019, 16:00 Europe/Stockholm

122:026 (Nordita, Stockholm)

Douglas Lundholm, Michele Correggi, Nicolas Rougerie

Venue

Nordita, Stockholm, Sweden

This will be a satellite event to the program "Spectral Methods in Mathematical Physics" of the Mittag-Leffler Institute which runs during January-April and includes a workshop on "Many-body theory, effective equations & PDE’s" in the following week, March 18-22. (See mittag-leffler.se/langa-program/spectral-methods-mathematical-physics)

Goal and purpose of the event

For quantum systems confined to lower-dimensional geometries there is a possibility to create states of matter that display very non-trivial topological behavior. The most famous example is the fractional quantum Hall effect and its associated effective particles with unusual statistics, called anyons. Despite such models having been studied intensively by physicists for a long time, there has been very little progress on the rigorous mathematical side. The aim of the workshop is therefore to bring together leading experts in the field, both mathematicians and physicists, to summarize the state of the art and to exchange ideas on future directions. In view of the serious theoretical intricacies of the field, particular emphasis will be put on the possible use of recent rigorous mathematics in physical applications.

Organizing committee

• Michele Correggi (Rome, Italy)
• Douglas Lundholm (Stockholm, Sweden)
• Nicolas Rougerie (Grenoble, France)

Scientific committee

• Stephane Ouvry (Orsay, France)
• Jan Philip Solovej (Copenhagen, Denmark)
• Susanne Viefers (Oslo, Norway)

Confirmed participants

• Joseph Avron (Technion, Haifa, Israel)
• Romain Duboscq (Toulouse, France)
• Giuseppe de Nittis (Santiago, Chile)
• Emanuela Giacomelli (Tübingen, Germany)
• Théotime Girardot (Grenoble, France)
• Gerald Goldin (Rutgers, USA)
• Gian Michele Graf (ETH Zurich, Switzerland)
• Oded Kenneth (Technion, Haifa, Israel)
• Edwin Langmann (Stockholm, Sweden)
• Simon Larson (Stockholm, Sweden)
• Jan Myrheim (Trondheim, Norway)
• Anne B. Nielsen (Dresden, Germany)
• Luca Oddis (Rome, Italy)
• Alessandro Olgiati (Grenoble, France)
• Gianluca Panati (Rome, Italy)
• Matthias Plaschke (Vienna, Austria)
• Alexios Polychronakos (New York, USA)
• Marcello Porta (Tübingen, Germany)
• Viktor Qvarfordt (Stockholm, Sweden)
• Steven Simon (Oxford, UK)
• Yoran Tournois (Stockholm, Sweden)
• Andrea Trombettoni (Trieste, Italy)
• Enderalp Yakaboylu (Vienna, Austria)
• Jakob Yngvason (Vienna, Austria)

Due to the limited capacity of the seminar room, please check with the organizers concerning possibility of participation.

Schedule with abstracts

Some nearby restaurants

Info about the dinner cruise on Thursday

Slides from the talks:

Arkeryd
Avron
Correggi
Duboscq
Goldin
Graf
Kenneth
Langmann
Larson
Nielsen
Oddis
Ouvry
Panati
Plaschke
Polychronakos
Porta
Qvarfordt
Rajaratnam
Tournois
Trombettoni
Yakaboylu
Yngvason

Sponsored by:

Sponsored by a prize from the Göran Gustafsson Foundation

Monday 11 March

10:00 → 10:30 Opening

10:30 → 11:20 (no title)

Speaker: J.P. SOLOVEJ

11:20 → 11:40 Coffee break

11:40 → 12:30 Group-Theoretical Approach to Anyons and Topological Quantum Configurations

Speaker: G. GOLDIN

12:30 → 14:30 Lunch Break

14:30 → 15:20 Emergent Gauge Fields and Anyons in Quantum Impurity Problems

Speaker: E. YAKABOYLU

15:20 → 15:40 Coffee break

15:40 → 16:30 Exclusion Bounds for Extended Anyons

Speaker: S. LARSON

16:40 → 17:30 The Calogero Model: Physics, Mathematics and Recent Results

Speaker: A. POLYCHRONAKOS

18:00 → 19:00 Reception

Tuesday 12 March

09:30 → 10:20 Anyons in Algebraic Quantum Field Theory

Speaker: J. YNGVASON

10:20 → 10:40 Coffee break

10:40 → 11:30 On Some Methods for the Numerical Simulation of Quantum Systems

Speaker: R. DUBOSCQ

11:40 → 12:30 The Boltzmann Haldane Equation for Anyons - Mathematical Results

Speaker: L. ARKERYD

12:30 → 14:30 Lunch Break

14:30 → 15:20 Deformed Calogero-Sutherland Model and Fractional Quantum Hall Effect

Speaker: E. LANGMANN

15:20 → 15:40 Coffee break

15:40 → 16:30 Vortex Lattice Solutions of the ZHK Chern-Simons Equations

Speaker: K. RAJARATNAM

16:40 → 17:30 Stability of the Laughlin Phase in Presence of Interactions

Speaker: A. OLGIATI

Wednesday 13 March

09:30 → 10:20 Quantized Hall Conductance for Large Interacting Systems

Speaker: J. AVRON

10:20 → 10:40 Coffee break

10:40 → 11:30 Anyons and Lowest Landau Level Anyons

Speaker: S. OUVRY

11:40 → 12:30 Local Anyon on the Universal Covering of the Circle leading to Cone-local Anyons on R^2

Speaker: M. PLASCHKE

12:30 → 19:30 Free afternoon

19:30 → 22:30 Social dinner

Thursday 14 March

09:30 → 10:20 Disorder and Topology. The Cases of Floquet and of Chiral Systems

Speaker: G.M. GRAF

10:20 → 10:40 Coffee break

10:40 → 11:30 Anyons in Fractional Quantum Hall Models

Speaker: A.B. NIELSEN

11:40 → 12:30 A Simple Model Leading to Nonabelian Anyon Behaviour

Speaker: O. KENNETH

12:30 → 14:30 Lunch Break

14:30 → 15:20 Quadratic Forms for Anyons

Speaker: L. ODDIS

15:20 → 15:40 Coffee break

15:40 → 16:30 Non-Abelian Anyons: Statistical Repulsion and Topological Quantum Computation

Speaker: V. QVARFORDT

16:40 → 17:30 Edge Universality in Interacting Topological Insulators

Speaker: M. PORTA

19:00 → 22:30 Dinner cruise

Friday 15 March

09:30 → 10:20 The Localization-Topology Correspondence: Periodic Systems and Beyond

Speaker: G. PANATI

10:20 → 10:40 Coffee break

10:40 → 11:30 Non-abelian Anyons in Paired Spin-singlet States

Speaker: Y. TOURNOIS

11:40 → 12:30 O-Diagonal Long-Range Order in Low-Dimensional Quantum Systems

Speaker: A. TROMBETTONI

12:30 → 14:30 Lunch Break

14:30 → 18:30 Discussions & closing