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.
- المعلم: Andreas Gleis
- المعلم: Kathrin Higgen
- المعلم: Seungsup Lee
- المعلم: Jheng-Wei Li
- المعلم: Jan von Delft