The MPI-PKS International School “Tensor Network based approaches to

Quantum Many-Body Systems” (TENSOR18) was held from 13 - 17

November 2018.

Tensor networks provide a new paradigm for describing quantum manybody

systems. This school covered recent progress in the fast moving field

of tensor network based simulations of quantum many-body systems. The

main goal of the school was to teach young PhD students the basics of

tensor-product states as well as the most recent technical developments.

This is particularly important given the increasing number of groups

working on this quickly evolving topic. The lectures and tutorials were given

by researchers who work actively both on the development and the

application on tensor-product state based methods.

The TENSOR18 school provided pedagogical introductions to matrixproduct

state based methods and discussed the most recent numerical

and analytical developments in the field. The school had lectures and

tutorials on different topics:

• Introduction to tensor networks and DMRG

(Lecturer: Steven R. White, UC Irvine)

• Tangent space methods for matrix product states

(Lecturer: Jutho Haegeman, Ghent)

• Two dimensional tensor networks

(Lecturer: Philippe Corboz, Amsterdam)

• Mathematical results and tools on Tensor Networks

(Lecturer: David Pérez García, Madrid)

• MPS methods for open systems

(Lecturer: Corinna Kollath, Aachen)

• MPS for Lattice Gauge Theories

(Lecturer: Mari Carmen Bañuls, Munich)

• Global Symmetries in Tensor Networks

(Lecturer: Claudius Hubig, Munich)

The school was very well received by the students and the feedback given

was extremely positive. The tutorials and hands-on sessions were

particular popular as these allowed a direct application of the theory taught

during the lectures. The lectures notes and tutorials are public and can be

accessed from the website of the European Tensor Network

(quantumtensor.pks.mpg.de).

The students participated very actively throughout the entire program and

the questions asked led to stimulating discussions. We were also happy to

see that the school helped students from different groups to get to know

each other which will foster future scientific exchange.

All students had the opportunity to present their own work during a poster

session. The poster session was very well attended and the students

discussed their work among each other and with the lectures until late

night.

Scientific Coordination: Frank Pollmann (TUM), Norbert Schuch (MPQ),

Ulrich Schollwoeck (LMU), and Frank Verstraete (Ghent)

Organization: Mandy Lochar from the MPI-PKS, Dresden