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Tensor Networks – Overview

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

Lecture: Monday 14:15 - 15:45, Wednesday 10:15 - 11:45 in room A450
Tutorial: Thursday 10:15 - 11:45 in room A450
Lecturer: Prof. Dr. Jan von Delft
Tutor: 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 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 numerical renormalization group (NRG) for treating quantum impurity models, the density matrix renormalization group (DMRG) for treating one-dimensional systems, and projected entangled pair states (PEPS) for treating two-dimensional quantum lattice models. 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.

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