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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 2021 (current)

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 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 is Michael Knap.

Content, Learning Outcome and Preconditions

Content

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

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

Preconditions

Quantum mechanics (PH0007) and statistical physics (PH0008) of the Physics Bachelor.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

TypeSWSTitleLecturer(s)DatesLinks
VO 2 Computational Methods in Many-Body Physics Knap, M. Pollmann, F. Tue, 14:00–16:00, PH 3343
and singular or moved dates
eLearning
UE 4 Exercise to Computational Methods in Many-Body Physics Hemery, K. Kadow, W. Lin, S. Wybo, E.
Responsible/Coordination: Knap, M.
singular or moved dates
and dates in groups
eLearning

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.

Media

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

Literature

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

Module Exam

Description of exams and course work

There will be a written exam of 90 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using calculation problems and comprehension questions.

For example an assignment in the exam might be: Which algorithm can be used to study an Ising phase transition?

Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.

There will be a bonus (one intermediate stepping of "0,3" to the better grade) on passed module exams (4,3 is not upgraded to 4,0). The bonus is applicable to the exam period directly following the lecture period (not to the exam repetition) and subject to the condition that the student passes the mid-term of actively participate in at least 75% of the tutorials

Exam Repetition

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

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