Some aspects of topology in condensed matter physics
Frequency
Every 2 years
Summary
Some topics covered in this class are: The Index theorem, solitons, topological band insulators/superconductors, bulk-edge correpondence, quantum anomalies, quantum pumping, symmetry protected topological phases and symmetry enriched topological order if time allows.
Content
In this class, I will give examples of phenomena in condensed matter physics that have a topological origin.
I will use the Su-Schrieffer-Heeger model for polyacetylene as the simplest fermionic Hamiltonian that ties concepts such as the index theorem, solitons, topological band insulator, the bulk-edge correspondence, quantum anomalies, and quantum pumping.
I will use the frustrated quantun spin-1/2 antiferromagnetic XYZ chain as the simplest Hamiltonian hosting continuous phase transitions that evade the Landau paradigm for phase transitions.
Other quantum spin Hamiltonians on a chain will be used to introduce the concept of symmetry protected topological phases.
If times allow, I will present the quantum spin-1/2 Kitaev Hamiltonian on a honeycomb and variant thereof to construct quantum spin liquids supporting topological order.
Learning Prerequisites
Recommended courses
The class will be self-contained and presumes no more than a solid grasp of quantum mechanics, say at the level of the textbook of Gordon Baym.
Resources
Bibliography
Christopher Mudry and Claudio Chamon
Fractionalization of Particles in Physics: Invertible Topological Phases of Matter (Cambridge University Press, 2025).
Ressources en bibliothèque
In the programs
- Exam form: Term paper (session free)
- Subject examined: Some aspects of topology in condensed matter physics
- Courses: 56 Hour(s)
- Type: optional