Tensor Networks: Mathematical Structures and Novel Algorithms

Overview

Tensor networks provide a new paradigm for efficiently describing quantum many body systems, based on the entanglement structure found in complex quantum many-body systems. They form the basis both for powerful numerical methods for the simulation of many-body problems and for a range of analytical tools for their study (see Background for more details). The goal of this programme is to bring together leading international experts from both mathematical and physical background who are working on the analytical and numerical aspects of tensor network states, in order to tackle the relevant open problems in the field, and to foster collaborations and exchange between the different approaches and communities.

Activities

During normal weeks throughout the thematic programme, there will be a very light program with very few scheduled informal discussions and talks, giving participants plenty of opportunity for intense collaborations.

In addition, there will two thematic workshops during the programme:

Finally, a school on "Tensor Network based approaches to Quantum Many-Body Systems", co-organized by the European Tensor Network, will be held alongside the program in the week of 5.-9. Sept. 2022. Further information on the school, including registration, can be found on the website of the school.

Workshop "Computational aspects of Tensor Networks"

The workshop, covering recent devepments on computations aspects of Tensor Networks, will take place 12.-16. Sept. 2022.

Confirmed speakers:

  • Natalia Chepiga
  • Philippe Corboz
  • Piotr Czarnik
  • Anna Francuz
  • Naoki Kawashima
  • Stefanos Kourtis
  • Andreas Läuchli
  • Örs Legeza
  • Esperanza López Manzanares
  • Ian McCulloch
  • Roger Mong
  • Simone Montangero
  • Ivan Oseledets
  • Didier Poilblanc
  • Jörg Schmiedmayer
  • Miles Stoudenmire
  • Luca Tagliacozzo
  • Antoine Tilloy
  • Atsushi Ueda
  • Laurens Vanderstraeten
  • Bram Vanhecke
  • Andreas Weichselbaum

Workshop "Mathematical structure of Tensor Networks"

The workshop, covering recent devepments on mathematical structure of Tensor Networks, will take place 3.-7. Oct. 2022.

Invited speakers:

  • Clement Delcamp
  • Jens Eisert
  • Paul Fendley
  • Jürgen Fuchs
  • Laurens Lootens
  • Angelo Lucia
  • Andreas Ludwig
  • Andras Molnar
  • Bruno Nachtergaele
  • Adam Nahum
  • Anne Nielsen
  • Yoshiko Ogata
  • Tobias Osborne
  • David Perez-Garcia
  • Christoph Schweigert
  • David Stephen
  • Hong-Hao Tu
  • Carolin Wille
  • Dominic Williamson
  • Erez Zohar

Background

Tensor networks provide a new paradigm for efficiently describing quantum many body systems. Some precursors of them already appeared in early works of Baxter when solving classical partition functions. In the late 80s, matrix product states (MPS) were discovered as powerful analytical tool to study the properties of quantum states. In this context, exact expressions of the seminal one-dimensional Affleck-Kennedy-Lieb-Tasaki (AKLT) state were found, which then gave rise to a broader class of so called finitely correlated states. Seemingly unrelated, a very important numerical development took place: White proposed in 1992 the famous density matrix renormalization group (DMRG) method, which quickly became the most powerful algorithm to simulate one-dimensional models. Only later on it was then realized that the computational power of DMRG can be understood in the framework of MPS representations, in particular, the DMRG algorithm variationally optimizes to quantum states in MPS form. The cross fertilization between the development of numerical methods and the discovery of analytical structures in Tensor Network has since revolutionized our understanding of emergent phenomena in quantum many body physics. Recent examples include the development of projected entangled pair states (PEPS) that extend the variational power of MPS to higher dimensions and provide a framework for the classification of phases of matter, the Multi-scale Entanglement Renormalization Ansatz  (MERA) that unravels the entanglement properties of critical states, and deep connections between tensor network states and the AdS/CFT correspondence in high energy physics.   

At the same time, the rapid development of the field has given rise to a plethora of new questions, both on the fundamental mathematical level and relating to their utility in simulating physical systems, ranging from the structure theory of tensor networks and the classification of phases, their relation to conformal field theories (CFTs), or their ability to describe black hole dynamics, all the way to the development of increasingly powerful numerical methods to simulate systems in an as diverse as possible set of scenarios, including higher dimensions, excitations, in particular also anyonic ones in topological phases, topological spin liquids, or lattice gauge theories.

The goal of this programme is to tackle the relevant open problems in the field, by bringing together leading international experts from both mathematical and physical background who are working on the analytical and numerical aspects of tensor network states, and to foster collaborations and exchange between the different approaches and communities.

 

This programme is supported by the European Research Council (ERC) through the ERC grant SEQUAM.

Aug. 29, 2022
14:00
Welcome and organisatorial meeting, Week 1

(Location: Schrödinger lecture hall, ESI)

Meetings during this week will be mostly organized informally. If you are not a registered participant, local, and would like to be kept in the loop about meetings in this week, please get in touch with Norbert Schuch.

Sept. 5, 2022
14:30
Welcome and organisatorial meeting, Week 2

(Location: Schrödinger lecture hall, ESI)

Meetings during this week will be mostly organized informally. If you are not a registered participant, local, and would like to be kept in the loop about meetings in this week, please get in touch with Norbert Schuch.

 

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Sept. 12.-16.: Workshop "Computational aspects of Tensor Networks"
(Location: Boltzmann lecture hall, ESI)
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Sept. 12, 2022
09:00 — 10:10
Registration and Welcome
10:10 — 11:00
Coffee break
11:00 — 11:45
12:30 — 14:30
Lunch break
15:15 — 15:45
Coffee break
Sept. 13, 2022
09:00 — 10:10
Stefanos Kourtis (UdeS)
Fast counting with tensor networks
Recording

(Blackboard talk)

10:10 — 11:00
Coffee break
11:00 — 11:45
11:45 — 12:30
Esperanza López Manzanares (UAM-CSIC, Madrid)
Algebraic Bethe Circuits
12:30 — 14:30
Lunch break
14:30 — 15:15
15:15 — 15:45
Coffee break
15:45 — 16:30
Luca Tagliacozzo (CSIC, Madrid)
Ablian LGT in 1D insights from MPS
16:30
Poster session
Sept. 14, 2022
09:00 — 10:10
Recording

(Blackboard talk)

10:10 — 11:00
Coffee break
11:00 — 11:45
11:45 — 12:30
12:30 — 14:30
Lunch break
14:30 — 15:15
15:15 — 15:45
Coffee break
15:45 — 16:30
Sept. 15, 2022
09:00 — 10:10
Recording

(Blackboard talk)

10:10 — 11:00
Coffee break
11:00 — 11:45
11:45 — 12:30
12:30 — 14:30
Lunch break
14:30 — 15:15
15:15 — 15:45
Coffee break
15:45 — 16:30
Laurens Vanderstraeten (Ghent U)
Spectral functions of 2-D quantum spin liquids
19:00
Conference dinner

Registration required. See your profile page for details and registration.

Sept. 16, 2022
09:00 — 10:10
10:10 — 11:00
Coffee break
11:45 — 12:30
Atsushi Ueda (ISSP, U of Tokyo)
Anatomy of 2D classical lattice models with TNR
Recording

 

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Sept. 19, 2022
11:00
Welcome and organisatorial meeting, week 4

(Location: Schrödinger lecture hall, ESI)

Meetings during this week will be mostly organized informally. If you are not a registered participant, local, and would like to be kept in the loop about meetings in this week, please get in touch with Norbert Schuch.
 

Sept. 26, 2022
13:30
Welcome and organsatorial meeting

(Location: Schrödinger lecture hall, ESI)

Meetings during this week will be mostly organized informally. If you are not a registered participant, local, and would like to be kept in the loop about meetings in this week, please get in touch with Norbert Schuch.


 

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Oct. 3.-7.: Workshop "Mathematical structure of Tensor Networks"
(Location: Boltzmann lecture hall, ESI)
*******************************************************************

Oct. 3, 2022
09:00 — 09:30
Registration and Welcome
09:30 — 10:15
10:15 — 10:50
Coffee break
10:50 — 12:00
Paul Fendley (U Oxford)
Defects and Duality on the Lattice

(Blackboard talk)

12:00 — 14:00
Lunch break
14:00 — 14:45
András Molnár (U Vienna)
TBA
14:45 — 15:30
Coffee break
15:30 — 16:40
Carolin Wille (U Oxford)
TBA

(Blackboard talk)

Oct. 4, 2022
09:00 — 10:10

(Blackboard talk)

10:10 — 10:50
Coffee break
10:50 — 12:00

(Blackboard talk)

12:00 — 14:00
Lunch break
14:45 — 15:30
Coffee break
15:30 — 16:40
David Pérez-García (U Complutense de Madrid)
Canonical forms and their applications in privacy

(Blackboard talk)

17:00
Poster session
Oct. 5, 2022
09:00 — 10:10
Jürgen Fuchs (U Karlstad)
String nets and RCFT correlators

(Blackboard talk)

10:10 — 10:50
Coffee break
10:50 — 12:00

(Blackboard talk)

12:00 — 14:00
Lunch break
14:00 — 14:45
14:45 — 15:30
Coffee break
19:00
Conference dinner

Registration required. See your profile page for details and registration.

Oct. 6, 2022
10:15 — 10:50
Coffee break
10:50 — 12:00
‪David T. Stephen (U of Colorado, Boulder)
TBA

(Blackboard talk)

12:00 — 14:00
Lunch break
14:00 — 14:45
Andreas Ludwig

TBA

14:45 — 15:30
Coffee break
15:30 — 16:40

(Blackboard talk)

Oct. 7, 2022
09:00 — 09:45
Anne Nielsen (AU)
TBA
09:45 — 10:30
Jens Eisert

TBA

10:30 — 11:15
Coffee break
11:15 — 12:25
Tobias Osborne (ITP Hannover)
Quantum Simulation of Conformal Field Theory

(Blackboard talk)

Organizers

Name Affiliation
Frank Pollmann Technical University of Munich
Norbert Schuch University of Vienna
Frank Verstraete Ghent University

Attendees

Name Affiliation
Juan Diego Arias Espinoza University of Amsterdam
Mark Arildsen University of California, Santa Barbara
Mari Carmen Banuls Max Planck Institute of Quantum Optics
David Blanik University Vienna
Pietro Brighi Institute of Science and Technology Austria
Nick Bultinck University of Oxford
Angela Capel University of Tübingen
Natalia Chepiga Technical University Delft
J. Ignacio Cirac Max Planck Institute of Quantum Optics
Philippe Corboz University of Amsterdam
Piotr Czarnik Jagiellonian University
Clement Delcamp Max Planck Institute, Dresden
Lukas Devos Ghent University
Jerôme Dubail University of Lorraine
Viktor Eisler Technische Universität Graz
Hans-Gerd Evertz Technische Universität Graz
Paul Fendley University of Oxford
Adrián Franco-Rubio Max Planck Institute of Quantum Optics
Anna Francuz University of Vienna
Jürgen Fuchs Karlstad University
Martin Ganahl SandboxAQ
Juan Garrahan University of Nottingham
José Garre Rubio University of Vienna
Albert Gasull Max Planck Institute of Quantum Optics
Andreas Gleis Ludwig-Maximilians-University Munich
Andrew Green University College London
David Kenworthy Gunn University of Innsbruck
Jutho Haegeman Ghent University
Juraj Hasik University of Amsterdam
Johannes Hauschild Technische Universität München
Fabian Heidrich-Meisner University of Göttingen
Michal P. Heller Ghent University
Michael Kastoryano IT University of Copenhagen
Naoki Kawashima University of Tokyo
Vladimir Kazeev University of Vienna
Stefanos Kourtis Université de Sherbrooke
Ilya Kull University of Vienna
Andreas Läuchli Paul Scherrer Institut, Villigen
Örs Legeza WIGNER RCP
Jheng-Wei Li Ludwig-Maximilians-University Munich
Jimin Li Universität Bonn
Shenghsuan Lin Technical University of Munich
Marko Ljubotina Institute of Science and Technology Austria
Laurens Lootens Ghent University
Esperanza López Manzanares Institute of Theoretical Physics UAM-CSIC
Faedi Loulidi University Paul Sabatier Toulouse
Angelo Lucia Universidad Complutense de Madrid
Andreas Ludwig University of California, Santa Barbara
Salvatore Manmana University of Göttingen
Ian McCulloch University of Queensland
Manuel Mekonnen University of Vienna
Frédéric Mila EPFL Lausanne
Gunnar Möller University of Kent
Frederik Møller Technical University of Vienna
András Molnár University of Vienna
Roger Mong University of Pittsburgh
Simone Montangero University of Padova
Bruno Nachtergaele University of California, Davis
Adam Nahum Ecole Normale Superieure
Anne Nielsen Aarhus University
Sen Niu University Paul Sabatier Toulouse
Reinhard Noack Philipps-Universität Marburg
Andreas Nunnenkamp University of Vienna
Yoshiko Ogata University of Tokyo
Tobias Osborne Institut für Theoretische Physik
Ivan Oseledets -
Zlatko Papic University of Leeds
David Pérez-García Universidad Complutense de Madrid
Didier Poilblanc University Paul Sabatier Toulouse
Cécile Repellin Laboratoire de Physique et Modélisation des Milieux Condensés
Matteo Rizzi University of Cologne
Markus Scheb Philipps-Universität Marburg
Jörg Schmiedmayer Technical University of Vienna
Ulrich Schollwöck Ludwig-Maximilians-University Munich
Christoph Schweigert University of Hamburg
Maksym Serbyn Institute of Science and Technology Austria
Jeongmin Shim Ludwig-Maximilians-University Munich
German Sierra Institute of Theoretical Physics UAM-CSIC
‪David T. Stephen University of Colorado
Miles Stoudenmire Flatiron Institute
Georgios Styliaris Max Planck Institute of Quantum Optics
Luca Tagliacozzo Consejo Superior de Investigaciones Científicas
Wei Tang Ghent University
Jordan Taylor University of Queensland
Antoine Tilloy MINES ParisTech
Hong-Hao Tu Technische Universität Dresden
Atsushi Ueda Institute for Solid State Physics - University of Tokyo
Laurens Vanderstraeten Ghent University
Bram Vanhecke University of Vienna
Jan von Delft Ludwig-Maximilians-University Munich
Andreas Weichselbaum Brookhaven National Laboratory
Carolin Wille University of Oxford
Dominic Williamson University of Sydney
Beatrix Wolf University of Vienna
Wen-Tao Xu University of Vienna
Mingru Yang University of Vienna
Amanda Young Technical University of Munich
Changkai Zhang Ludwig-Maximilians-University Munich
Erez Zohar The Hebrew University of Jerusalem
Preview of Stefanos Kourtis - Fast counting with tensor networks
Stefanos Kourtis (UdeS): Fast counting with tensor networks
Sept. 13, 2022 09:00 — 10:10
Preview of Esperanza López Manzanares - Algebraic Bethe Circuits
Esperanza López Manzanares (UAM-CSIC, Madrid): Algebraic Bethe Circuits
Sept. 13, 2022 11:45 — 12:30
Preview of Miles Stoudenmire - Disentangling Interacting Systems with Gaussian Tensor Networks
Miles Stoudenmire (Flatiron Inst., New York): Disentangling Interacting Systems with Gaussian Tensor Networks
Sept. 13, 2022 14:30 — 15:15
Preview of Luca Tagliacozzo - Ablian LGT in 1D insights from MPS
Luca Tagliacozzo (CSIC, Madrid): Ablian LGT in 1D insights from MPS
Sept. 13, 2022 15:45 — 16:30
Preview of Antoine Tilloy - Attacking 1+1 dimensional field theories with relativistic CMPS
Antoine Tilloy (MINES ParisTech): Attacking 1+1 dimensional field theories with relativistic CMPS
Sept. 14, 2022 09:00 — 10:10
Preview of Bram Vanhecke - Continuous Tensor Networks for Lattice Models
Bram Vanhecke (U Vienna): Continuous Tensor Networks for Lattice Models
Sept. 14, 2022 11:00 — 11:45
Preview of Philippe Corboz - iPEPS for 3D and layered quantum systems
Philippe Corboz (U Amsterdam): iPEPS for 3D and layered quantum systems
Sept. 14, 2022 11:45 — 12:30
Preview of Piotr Czarnik - iPEPS simulations of strongly correlated systems at finite temperature
Piotr Czarnik (Jagiellonian U, Krakow): iPEPS simulations of strongly correlated systems at finite temperature
Sept. 14, 2022 14:30 — 15:15
Preview of Didier Poilblanc - Simulating chiral spin liquids with projected entangled-pair states
Didier Poilblanc (U Paul Sabatier, Toulouse): Simulating chiral spin liquids with projected entangled-pair states
Sept. 14, 2022 15:45 — 16:30
Preview of Naoki Kawashima - Tensor-network-representable quantum states
Naoki Kawashima (U Tokyo): Tensor-network-representable quantum states
Sept. 15, 2022 09:00 — 10:10
Preview of Andreas Läuchli - Accurate CFT data and velocities from iMPS simulations
Andreas Läuchli (PSI, Villigen): Accurate CFT data and velocities from iMPS simulations
Sept. 15, 2022 11:45 — 12:30
Preview of Frederik Møller - Emergent hydrodynamics and Pauli blocking in a 1D Bose gas
Frederik Møller (TU Vienna): Emergent hydrodynamics and Pauli blocking in a 1D Bose gas
Sept. 15, 2022 14:30 — 15:15
Preview of Atsushi Ueda - Anatomy of 2D classical lattice models with TNR
Atsushi Ueda (ISSP, U of Tokyo): Anatomy of 2D classical lattice models with TNR
Sept. 16, 2022 11:45 — 12:30
At a glance
Type:
Thematic Programme
When:
Aug. 29, 2022 — Oct. 21, 2022
Where:
ESI Boltzmann Lecture Hall
Organizer(s):
Frank Pollmann (TU Munich)
Norbert Schuch (U Vienna)
Frank Verstraete (Ghent U)
More:
Website