Syllabus

Topics:

  • Interacting electrons in 1D
  • Bosonization and its applications
  • The renormalization group
  • Interacting fermions in D>1: Fermi liquids and their instabilities
  • Quantum phase transitions
  • Gauge theories and their applications in condensed matter
  • The quantum Hall effect


Bibliography:

  • Renormalization group for bosons and fermions: R. Shankar, "Renormalization-group approach to interacting fermions", Reviews of Modern Physics 66, 129 (1994).
  • Bosonization: T. Giamarchi, "Quantum Physics in One Dimension".
  • Quantum (and classical) phase transitions: S. Sachdev, "Quantum Phase Transitions" (2nd edition, 2011).
  • Lattice gauge theory: J. Kogut, "An introduction to lattice gauge theory and spin systems", Reviews of Modern Physics 51, 659 (1979).
  • Spin liquids and Kitaev's toric code: L. Savary and L. Balents, "Quantum Spin Liquids", https://arxiv.org/pdf/1601.03742.pdf.