Computational Methods in Many-Body Physics (PH2264)
Lecturers: Michael Knap, Frank Pollmann
Teaching Assistant: Wilhelm Kadow, Bernhard Jobst, Raul Morral Yepes, Philip Zechmann
Lectures: Tue 16:00-17:30
Practicals: Fri 14:00-18:00
This course provides an introduction to numerical techniques used for solving quantum many-body problems. It covers (Quantum) Monte Carlo, Exact Diagonalization, Matrix Product States, Tensor Networks, and Non-Equilibrium Quantum Field Theory. This course is highly interactive. It consists of two hours lectures per week accompanied by four hours of practicals in which the newly acquired techniques will be applied to problems that directly touch upon current research in our groups.
The course will be offered this semester at the announced times and will be based on web conferencing. Further details will be sent by email to all participants registered in campus online. Please sign up online to be able to receive the latest information.
II. Classical Monte Carlo simulations
Critical slowing down: cluster and loops algorithm
III. Finite size scaling analysis
IV. Exact diagonalization
Sparse matrices and the Lanczos method
V. Entanglement and matrix product states
Scaling in critical systems
VI Matrix product state based algorithms
Time Evolving Block Decimation
Density Matrix Renormalization Group
VII. Tensor product states
VIII. Machine Learning
Exercises and solutions will be provided on Moodle.
You will be given time to solve the exercises during the Friday tutorials.
To get a bonus for the final exam, show up to the Friday tutorials or send some codes/plots to a TA to prove that you worked on the exercises.
Introduction to Python, www.scipy-lectures.org/
Lecture Notes by Anders W. Sandvik, http://arxiv.org/abs/1101.3281v1
Lecture Notes by Johannes Hauschild, Frank Pollmann, https://arxiv.org/abs/1805.00055
Review on DMRG by Ulrich Schollwoeck, arxiv.org/abs/1008.3477
Online book by Michael Nielsen, http://neuralnetworksanddeeplearning.com
We will give out numerical projects, which are extensions of the tutorials.
Students, who want to take the exam, need to choose and work on one of these projects.
In the oral exam, the students are asked to give a 10 minutes presentation on the basic ideas and results of the project, followed by 15 minutes of questions, which can be both about the project itself as well as general questions regarding other topics of the course.