- Symmetry breaking and phase transitions: Landau theory.
- Critical phenomena at classical thermal phase transitions.
- Two dimensional superfluids, the classical Kosterlitz-Thouless transition, and duality.
- Classical XY-vortex duality in three dimensions.
- Fermi liquids and quasiparticles.
- Quantum matter in one dimension: Tomonaga Luttinger liquids.
- Quantum phase transitions of bosons: Quantum Ising model and the superfluid-insulator transition.
- Quantum phase transitions of fermions: Hubbard model on the honeycomb and square lattices.
-
Z2 gauge theories: confinement-deconfinement transitions, topological order, and interplay with symmetry breaking.
- Spin liquids: emergent gauge fields and Higgs phases.
- Fractional quantum Hall states: fermion-vortex duality, composite fermions, and Chern- Simons gauge theories.
- Non-Fermi liquids.
- The SYK model: strange metals and black holes.
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