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)

Education

MSc Programme in Physics

Learning outcome

Knowledge:
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.

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

Competences:
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.

ECTS
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.
Aid
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