Max Planck Institute for the Physics of Complex Systems: Teaching

Theory of Quantum Magnetism (WiSe 2025/26)

Lecturer: Alexander Wietek

When we think of magnetism, the familiar ferromagnet often comes to mind. Yet magnetism hosts far richer phenomena: antiferromagnets with alternating spins, topological textures like skyrmions, and the newly discovered altermagnets. Beyond these ordered states, quantum fluctuations can even prevent spins from settling altogether, giving rise to exotic quantum spin liquids. Magnetism, therefore, is not just a simple alignment of spins, but a vast playground of diverse and fascinating quantum phenomena.

In this lecture, we explore the theoretical foundations of the different forms of magnetism. We examine the quantum mechanical origins of magnetic interactions and provide an overview of the collective magnetic states that can emerge at the macroscopic level. Key mathematical results, such as the Mermin–Wagner theorem and the Lieb–Schultz–Mattis–Hastings theorem, are introduced and discussed in the context of quantum magnets. We then present an introduction to spin-wave theory and its applications, before turning to the theory of quantum spin liquids and the concept of topological order.

Prerequisites: Electromagnetism, Statistical Physics

Time and Place:

Friday: 11:10 - 12:40
Venue: Seminar Room 4 (SR4), Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str 38, Dresden 01187

Lecture Notes: “Complete Lecture Notes”

Syllabus:

Date	Lecture Topic	Material
Oct 17	Introduction Solution of the one-dimensional Ising model	Notes: “Course Overview and Classical Spin models”
Oct 24	Spin-Spin correlation functions, correlation length, domain wall excitations and scale invariance in the one-dimensional Ising model	Notes: “Lecture 2”
Nov 7	The two-dimensional Ising model and the Kramers-Wannier duality.	Notes: “Lecture 3”
Nov 14	Two-dimensional transfer matrix solution.	Notes: “Lecture 4”
Nov 21	Spin operator algebras, Canonical transformations of spins, Jordan-Wigner transformation and the fermion operator algebra.	Notes: “Lecture 5”
Nov 28	Canonical transformations of fermions and diagonalization of the transfer matrix.	Notes: “Lecture 6”
Dec 12	Properties of the square lattice Ising model, Geometric frustration and Transverse-field Ising model	Notes: “Lecture 8”
Jan 9	Transverse-field Ising model (continued)	Notes: “Lecture 9”
Jan 16	Gapped phase of matters and Lieb-Robinson bounds	Notes: “Lecture 10”
Jan 23	Lieb-Robinson bounds (continued)	Notes: “Lecture 11”
Jan 30	Spectral flow theorem	Notes: “Lecture 12”
Feb 6	Spectral flow theorem (continued), the Heisenberg model, Marshall’s theorem and Spontaneous symmetry breaking	Notes: “Lecture 13/14”