Course Syllabus


  • 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.
  • Zgauge 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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