PHYS-638 / 4 credits

Teacher: Mudry Christopher Marc

Language: English

Remark: Next time: Fall 2025


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

Reference week

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