Tensor Networks 2021 – Overview
Prof. Dr. Jan von Delft, LS Theoretical solid state physics
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.