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:

• 12.-16. Sept. 2022: Workshop "Computational aspects of Tensor Networks"
• 3.-7. Oct. 2022: Workshop "Mathematical structure of Tensor Networks"

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:

• 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.