Quantum Magnetism (PH2310)

Lecturer: Johannes Knolle
Teaching Assistants: Stefan Birnkammer, Hui-Ke Jin, Valentin Leeb, Gibaik Sim

Lectures: Tuesday 8:00 - 10:00; Thursday 12:00 - 14:00
Tutorials: Wednesday 16:00 - 18:00; ; Thursday 12:00 - 14:00 


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


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

TUM Course Website PH2310