Quantum Magnetism

Course content

The course covers modern developments in quantum magnetism, introducing concepts, theory, numerical tools, and experimental techniques. The course comprises:

  • Corrections to the classical picture of magnetism (spin wave theory, bound spin waves, phase transitions, and magnetic thermodynamics)
  • Solvable quantum systems (1D Ising model, 1D XY chain, 1D Heisenberg chain, Small systems, dimerized systems, 2D Ising model on the square lattice)
  • Quantum phase transitions (the general concept, 1D Ising model in a transverse field, 2D and 3D systems, complex systems, e.g. superconductivity)
  • Frustration (2D triangular Ising model, Anderson RVB, Order from disorder, Spin liquid and spin ice)
  • Numerical techniques (Spin wave theory code SpinW, Exact diagonalization code RLexact, high-temperature expansion, Quantum Monte Carlo code ALPS)

Experimental techniques (susceptibility and magnetization, heat capacity, NMR, muon spin rotation, neutron scattering)


MSc Programme in Physics

Learning outcome

The students aquire an understanding of current solved and unsolved problems in many-body quantum mechanics, exemplified in quantum magnets. They also obtain an uderstanding of particular current topics as quantum phase transitions and frustration in magnetism.

The students become proficient with a number of theoretical methods, including mean-field theory, spin wave theory, high-temperature expansion, and exact diagonalization.

In addition, the students are capable of interpreting and modeling data from a number of experimental techniques, including susceptibility, heat capacity, and neutron scattering.

Lectures, problems, student presentations, and projects

(is picked from)

  • S. Blundell: Magnetism in Condensed matter (background from magnetism course)

  • K. Lefmann: Neutron scattering (magnetism course notes or Neutron course notes)

  • K. Yosida: Theory of Magnetism

  • D.C. Mattis: Magnetism made simple

  • S. Sachdev: Quantum Phase Transitions

  • Original articles

See Absalon for final course material.

Knowledge of basic solid state physics and magnetism at M.Sc. level. Knowledge corresponding to the contents of the courses condensed matter physics 1 and 2.

Academic qualifications equivalent to a BSc degree is recommended.

Continuous feedback during the course of the semester

Individual oral feedback on the two mandatory colloquia during the course. Collective, written feedback on the final report.

7,5 ECTS
Type of assessment
Written assignment, 4 weeks
Project report, possibly 2-person groups. The students have 4 weeks (parallel to the teaching) to work on the project, which should be handed in in the exam week.
All aids allowed
Marking scale
passed/not passed
Censorship form
No external censorship
The course responsible plus one person.
Criteria for exam assessment

see learning outcome

Single subject courses (day)

  • Category
  • Hours
  • Class Instruction
  • 40
  • Exercises
  • 40
  • Colloquia
  • 40
  • Project work
  • 86
  • English
  • 206