Tensor Networks 2021 – Overview

Prof. Dr. Jan von Delft, LS Theoretical solid state physics

Lecture: Wednesday 12:15 - 13:45 , Thursday 14:15 - 15:45 (zoom)
Tutorial: Tuesday 12:15 - 13:45 (zoom)
Lecturer: Prof. Dr. Jan von Delft
Tutor: Andreas Gleis, Seung-Sup Lee, Jheng-Wei Li

During the last two decades, tensor networks have emerged as a powerful new language for encoding the wave functions of quantum many-body states, and the operators acting on them, in terms of contractions of tensors. Insights from quantum information theory have led to highly efficient and accurate tensor network representations for a variety of situations, particularly for one- and two-dimensional (1d, 2d) systems. For these, tensor network-based approaches rank among the most accurate and reliable numerical methods currently available.

This course offers an introduction to tensor network-based numerical methods, including
- the density matrix renormalization group (DMRG) for 1d quantum lattice models,
- the numerical renormalization group (NRG) for quantum impurity models,
- pair-wise entangled pair states (PEPS) for 2d quantum lattice models,
- the tensor renormalization group (TRG) for 2d classical lattice models,
- the exponential TRG (XTRG) for 1d models at finite temperature.

Topics treated in lecture will be supplemented by working MATLAB codes provided in the tutorials. By studying these codes in detail and adapting them to solve concrete physics problems, students will gain practical, hands-on working knowledge of tensor network coding. The exam will consist of a take-home problem involving writing your own code to reproduce some results from recently published research papers.