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

1 Opening

2 (no title)

Speaker: J.P. SOLOVEJ

3 Coffee break

4 Group-Theoretical Approach to Anyons and Topological Quantum Configurations

Speaker: G. GOLDIN

5 Lunch Break

6 Emergent Gauge Fields and Anyons in Quantum Impurity Problems

Speaker: E. YAKABOYLU

7 Coffee break

8 Exclusion Bounds for Extended Anyons

Speaker: S. LARSON

9 The Calogero Model: Physics, Mathematics and Recent Results

Speaker: A. POLYCHRONAKOS

10 Reception

Tuesday 12 March

11 Anyons in Algebraic Quantum Field Theory

Speaker: J. YNGVASON

12 Coffee break

13 On Some Methods for the Numerical Simulation of Quantum Systems

Speaker: R. DUBOSCQ

14 The Boltzmann Haldane Equation for Anyons - Mathematical Results

Speaker: L. ARKERYD

15 Lunch Break

16 Deformed Calogero-Sutherland Model and Fractional Quantum Hall Effect

Speaker: E. LANGMANN

17 Coffee break

18 Vortex Lattice Solutions of the ZHK Chern-Simons Equations

Speaker: K. RAJARATNAM

19 Stability of the Laughlin Phase in Presence of Interactions

Speaker: A. OLGIATI

Wednesday 13 March

20 Quantized Hall Conductance for Large Interacting Systems

Speaker: J. AVRON

21 Coffee break

22 Anyons and Lowest Landau Level Anyons

Speaker: S. OUVRY

23 Local Anyon on the Universal Covering of the Circle leading to Cone-local Anyons on R^2

Speaker: M. PLASCHKE

24 Free afternoon

25 Social dinner

Thursday 14 March

26 Disorder and Topology. The Cases of Floquet and of Chiral Systems

Speaker: G.M. GRAF

27 Coffee break

28 Anyons in Fractional Quantum Hall Models

Speaker: A.B. NIELSEN

29 A Simple Model Leading to Nonabelian Anyon Behaviour

Speaker: O. KENNETH

30 Lunch Break

31 Quadratic Forms for Anyons

Speaker: L. ODDIS

32 Coffee break

33 Non-Abelian Anyons: Statistical Repulsion and Topological Quantum Computation

Speaker: V. QVARFORDT

34 Edge Universality in Interacting Topological Insulators

Speaker: M. PORTA

35 Dinner cruise

Friday 15 March

36 The Localization-Topology Correspondence: Periodic Systems and Beyond

Speaker: G. PANATI

37 Coffee break

38 Non-abelian Anyons in Paired Spin-singlet States

Speaker: Y. TOURNOIS

39 O-Diagonal Long-Range Order in Low-Dimensional Quantum Systems

Speaker: A. TROMBETTONI

40 Lunch Break

41 Discussions & closing