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Computational Methods in Many-Body Physics

Module PH2264

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of SS 2018

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 2022SS 2021SS 2020SS 2019SS 2018

Basic Information

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
  • Focus Area Theoretical Quantum Science & Technology in M.Sc. Quantum Science & Technology
  • 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 workloadContact hoursCredits (ECTS)
300 h 90 h 10 CP

Responsible coordinator of the module PH2264 in the version of SS 2018 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 course: 

• 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

Learning Outcome

After successful completion of the module the students are able to:

  1. know and reflect the recent developments and open questions in computational many-body physics
  2. understand state-of-the-art numerical techniques applied in condensed matter theory
  3. judge which numerical method is best suited to sovle a new problem
  4. program non-trivial codes in python


Quantum mechanics and statistical physics of the Physics Bachelor.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

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 the supervision of a tutor 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,
Lecture Notes by Anders W. Sandvik,
Lecture Notes by Johannes Hauschild, Frank Pollmann,
Review on DMRG by Ulrich Schollwoeck,
Lecture Notes by Juergen Berges,
Online book by Michael Nielsen,

Module Exam

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 presentations independently prepared by the students. The exam of 25 minutes consists of the presentation and a subsequent discussion.

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.

Exam Repetition

The exam may be repeated at the end of the semester.

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