Computational Methods in Many-Body Physics
Module version of SS 2020
There are historic module descriptions of this module. A module description is valid until replaced by a newer one.
Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.
|available module versions|
|SS 2021||SS 2020||SS 2019||SS 2018|
PH2264 is a semester module in English or German language at Master’s level which is offered in winter semester.
This Module is included in the following catalogues within the study programs in physics.
- Theory courses for condensed matter physics
- Theory courses for Applied and Engineering Physics
- Complementary catalogue of special courses for nuclear, particle, and astrophysics
- Complementary catalogue of special courses for Biophysics
- Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)
If not stated otherwise for export to a non-physics program the student workload is given in the following table.
|Total workload||Contact hours||Credits (ECTS)|
|300 h||90 h||10 CP|
Responsible coordinator of the module PH2264 in the version of SS 2020 was Michael Knap.
Content, Learning Outcome and Preconditions
This module provides an introduction to numerical methods for the simulation of classical and quantum many-particle systems. A focus lies on the investigation of model systems that describe strongly correlated quantum matter. The emergent physical phenomena in such system are often out of reach for analytical approaches and thus numerical approaches are essential for their understanding. The following methods will be covered in the module:
• Classical Monte Carlo simulations
• Finite size scaling analysis
• Exact diagonalization
• Many body entanglement
• Matrix product states
• Tensor product states
• Quantum Monte Carlo methods
• Non-equilibrium field theory
After successful completion of the module the students are able to:
- know and reflect the recent developments and open questions in computational many-body physics
- understand state-of-the-art numerical techniques applied in condensed matter theory
- judge which numerical method is best suited to sovle a new problem
- program non-trivial codes in python
Quantum mechanics (PH0007) and statistical physics (PH0008) of the Physics Bachelor.
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
|VO||2||Computational Methods in Many-Body Physics||Knap, M. Pollmann, F.||
Tue, 14:00–16:00, PH 3343
|UE||4||Exercise to Computational Methods in Many-Body Physics||
Responsible/Coordination: Knap, M.
|dates in groups||
Learning and Teaching Methods
The modul consists of a lecture and exercise classes.
The lecture is designed for the presentation of the subject, usually by blackboard presentation. The focus resides on theoretical foundations of the field, presentation of methods and simple, illustrative examples. Command of basic methods is deepened and practised through homework problems, which cover important aspects of the field. The homework problems should develop the analytic skills of the students and their ability to perform calculations. The homework problems are discussed in the exercises by the students themselves under supervision in order to develop the skills to explain a physics problem logically.
Oral presentation, blackboard work, lecture notes as PDF for download, beamer presentation, exercise sheets, problems to solve on the PC, accompanying website to the lecture
Introduction to Python, www.scipy-lectures.org
Lecture Notes by Anders W. Sandvik, arxiv.org/abs/1101.3281v1
Lecture Notes by Johannes Hauschild, Frank Pollmann, arxiv.org/abs/1805.00055
Review on DMRG by Ulrich Schollwoeck, arxiv.org/abs/1008.3477
Lecture Notes by Juergen Berges, arxiv.org/abs/1503.02907
Online book by Michael Nielsen, neuralnetworksanddeeplearning.com
Description of exams and course work
The achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using final projects independently prepared by the students. The exam of about 25 minutes consists of the presentation of the project’s results and a subsequent oral exam.
For example an assignment in the exam might be:
- Implement the N-state Potts model using Monte Carlo.
- Study the critical behavior of the (classical) 3D Ising model using the Swendsen-Wang algorithm.
- Program the Krylov time evolution for a random Heisenberg chain.
- Construct the reduced density matrix from MPS.
Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.
The exam may be repeated at the end of the semester.