Topology in condensed matter physics

Zoom-link

Lecture in winter term 2024.
Lecturer: Thore Posske
Course assistent: Anna Junker

Script

Script of current course

Organization


Schedule:
Lecture: Wed, 10:00 a.m. - 11:30 a.m., Notkestr. 9, SemRm 4064
Exercises: Wed, 1:00 p.m. - 2:30 p.m., Notkestr. 9/11, SemRm 4024
No lecture: Oct 30 and Dec 25, Jan 1 (Christmas & new year)
Last lecture: Wed, Jan 29, 2025.
Topics, recommendations, and literature
Consent for video recording
Zoom-link

Exam

Exam oral or written, date to be determined


There will be a Questions and Answers session the Wednesday before the exam starting at 10:00 a.m.. Please send questions in advance.

Content

toggler: ↑ less ↑

Additional material

Video lecture by John Milnor (Fields medalist, "Milnor spheres") about differential topology
Video lectures by Norman Wildberger about algebraic topology explained very intuitively
Video that the torus can be folded to a Moebius strip and
corresponding Mathematica notebook
Notebook for numerically experimenting with the Kitaev chain's spectrum and topological phases

Recommended reading/references

Topology In Condensed Matter: An Introduction - Miguel A N Araujo and Pedro Sacramento
Quantum Computation and Quantum Information - Michael Nielsen and Isaac Chuang


Altland's and Simons' book on Condensed Matter theory
Course on topology in condensed matter physics by Akhmerov et al.

Topology and physics - a historical essay, C. Nash
Topological Quantum Computation-From Basic Concepts to First Experiments, Stern, Ady and Lindner, Netanel H.
Seminal paper of Leinaas and Myrheim '77 describing anyons
Philosophical background on the "principle of indiscernibles"
Kitaev's periodic table of gapped, non-interacting, topological phases
Ryu, Schnyder, Furusaki, Ludwig, classification of gapped, non-interacting, topological phases
Katos seminal paper about adiabatic time evolution