PHYSICS 268R: Quantum Phases of Matter

PHYSICS 268R: Quantum Phases of Matter

A course on modern topics in the quantum phases of matter. 

Pre-requisites: graduate courses in quantum mechanics and statistical mechanics, including familiarity with second quantization and path integrals.

    1. The interacting Fermi gas: quasiparticles, and an elementary introduction to Fermi liquid theory.
    2. The interacting Bose gas: Bogoliubov theory and superfluidity.
    3. BCS theory of superconductivity.
    4. The Bose Hubbard model: insulators and superfluids
    5. Quantum Ising models, field theories, correlation functions, and quantum criticality without quasiparticles.
    6. Interacting bosons in two dimensions: fractionalization, and the Z2 spin liquid.
    7. Quantum Ising gauge theories. Duality. Topological order.
    8. Interacting fermions and bosons in one dimension: the Tomonaga-Luttinger liquid
    9. The integer quantum Hall effect.
    10. Berry phases, band topology, and Chern insulators.
    11. Chern-Simons gauge theories and topological order.
    12. U(1) gauge theories of spin liquids: the chiral spin liquid.
    13. Fractional quantum Hall states: Laughlin and Jain
    14. Ising anyons and non-Abelian topological order
    15. Dualities of XY models and U(1) gauge theories
    16. Application of dualities to spin liquids
    17. Boson-fermion and fermion-fermion dualities
    18. Gapless spin liquids

Section: Weekly on Tuesdays 4-5pm. We will discuss additional materials as well as homework. 

TF Office hour: I will not hold regular office hours. I will be on slack regularly to address questions. If you feel comfortable, I encourage you to post questions on public discussion channel as someone else might share the same confusion and learn from your question. Private message is also fine. You can also schedule Zoom meeting with me if you prefer.