Special exercise
This is an individual exercise, and it will be related with one or several topics of the lectures. The exercise is expected to take on the order 5-6 pages to solve, and it can be analytical, numerical or qualitative. You are supposed to do the special exercises on your own. You are free to do what you consider most interesting within the context of one of the topics listed below, for example writing an essay on it.
List of special exercises:
- The Anderson-Higgs mechanism in superconductors
- Luttinger liquid and spin-charge separation
- Dirac physics in graphene
- The four-dimensional quantum Hall effect
- Magnetic interactions in oxides, the Goodenough-Kanamori rules
- Topological quantum computing with non-abelian anyons
- Spin ice and emergent gauge theory
- The toric code and topological degeneracy
- The spin transistor
- Higher order topological insulators
- Mechanisms for multiferroicity
- Non-hermitian topological insulators
- Time-dependent density functional theory
- Superconducting density functional theory
- Machine learning with many-body tensor networks
- Reinforcement learning in physics