Tensor networks: from basics to tangent space – Overview

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

Lecture: Wednesday 12:15 - 13:45 , Thursday 14:15 - 15:45 (hybrid = classroom + zoom)
Tutorial: Tuesday 12:15 - 13:45 (hybrid)
(On the first Tuesday of the semester, 26.04.22, there will be a lecture instead of a tutorial.)
Lecturer: Prof. Dr. Jan von Delft
Tutor: Sasha Kovalska, Marc Ritter, Markus Scheb, Jeongmin Shim

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,
- quantics tensor cross interpolation (QTCI) for multivariate functions.

Topics treated in lecture will be supplemented by tutorials, entailing both questions to be answered in writing and coding problems to be solved by writing code in MATLAB or Julia. Solution codes will be provided (post due date) for all coding problems. In this manner, students will gain practical, hands-on working knowledge of tensor network coding.

Prequisites: Linear Algebra, Quantum Mechanics I, Statistical Physics I. Some knowledge of Many-Body Physics would be helpful, but is not required.