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Quantum Magnetism

Module PH2310

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.

Basic Information

PH2310 is a semester module in English language at which is offered in summer semester.

This Module is included in the following catalogues within the study programs in physics.

  • Specific catalogue of special courses for condensed matter 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
  • Complementary catalogue of special courses for Applied and Engineering Physics
  • 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 PH2310 is Johannes Knolle.

Content, Learning Outcome and Preconditions


Magnetism has been known for millennia but a microscopic understanding has only emerged with the advent of Quantum Mechanics in the last century. This module introduces the basic concepts of quantum magnetism and the theoretical description of magnetic quantum phases of matter. Apart from foundational concepts for long-range ordered ferro- and antiferro-magnetic phases, the lecture covers latest developments in the description of strongly correlated quantum magnets, for example spin fractionalization in quantum spin liquids.

The following topics will be covered in the module:

    Magnetic moments and exchange interactions
    Types of magnetic order and spin waves
    Topological magnon insulators
    Magnetism in metals
    The Hubbard model: Stoner FM and spin density wave AFM
    Kondo effect, heavy fermions and Doniach's phase diagram
    Frustrated Magnetism
    Classical and quantum order by disorder
    Quantum spin liquids and Fractionalization
    Kitaev spin liquids and candidate materials

Learning Outcome

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

    ...know and classify different types of magnetism
    ...perform spin wave calculations and calculate spin structure factors
    ...understand the different contributions to the magnetic response of metals
    ...perform calculations for the FM and AFM phases of the Hubbard model
    ...understand the origin of magnetic frustration, non-bipartite lattices and competing interactions
    ...understand quantum order by disorder
    ...perform parton mean field calculation for describing quantum spin liquids
    ...know the origin of spin fractionalization and its experimental consequences
    ...understand the Majorana fermion solution of Kitaev models
    ...know about candidate materials and experimental signatures of quantum magnets


In addition to the requirements for the Master’s program in Physics an understanding of second quantization and quantum statistical mechanics is needed.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 4 Quantum Magnetism Knolle, J. Tue, 08:00–10:00, virtuell
Fri, 10:00–12:00, virtuell
UE 2 Exercise to Quantum Magnetism Jin, H. Sim, G. Willsher, J.
Responsible/Coordination: Knolle, J.

Learning and Teaching Methods

The main topics and theoretical tools are presented in the lectures, usually in a blackboard style presentation. The application of basic methods and additional specialised techniques are covered in the tutorials. The homework problems are designed to develop the analytic skills of the students and it is expected that solutions are presented and discussed in the tutorial classes.


Blackboard lectures, written notes for download, exercise sheets


The following books and advanced reviews will be used:

    A. Auerbach: Interacting Electrons and Quantum Magnetism
    P. Fazekas: Lecture Notes on Electron Correlation and Magnetism
    S. Blundell: Magnetism in Condensed Matter
    P. Coleman: Introduction to Many-Body Physics
    H.T. Diep (Ed.): Frustrated Spin Systems
    C. Lacroix et al. (Eds.): Introduction to Frustrated Magnetism
    X.-G. Wen: Quantum Field Theory of Many-Body Systems
    Knolle and Moessner: A Field Guide to Spin Liquids
    Savary and Balents: Quantum Spin Liquids

Module Exam

Description of exams and course work

There will be an oral exam of 30 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample calculations.

For example an assignment in the exam might be:

  • Explain the basics of parton descriptions of quantum spin liquids and its relation to spin fractionalization
  • Explain the basic idea for quantum order by disorder and how to treat it microscopically
  • Explain the SDW phase of the half filled Hubbard model and its excitations

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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