TQM Lectures 2022

These are the slides from Michaelmas 2022. If you want a nice printable version for saving as a PDF, you can use e.g. austen.uk/lectures/many-body-wavefunctions/?print-pdf#/

If you ever want access to the $\LaTeX$ for the mathematical expressions, right click and select Show Math As > TeX Commands

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Interested in theoretical condensed matter research?

Summer internships are available at the Max Planck Institute for the Physics of Complex Systems in Dresden

Projects in TCM for October 2023 entry


  • Take place in the Small Lecture Theatre at the Cavendish Laboratory from 09.30-11.00 on Tuesdays and Thursdays.


  • Many Body Wavefunctions

    Product States. Fermi gas. Density, density matrix, and pair distribution.

  • Quantum Hall Effect

    Landau levels. Laughlin wavefunction. Fractional charge, Fractional statistics.

  • The Elastic Chain

    Quantizing a chain. Ground state displacement fluctuations. statistics.

  • Spin Models

    Heisenberg model. Heisenberg chain. Magnons. Antiferromagnets. Symmetry breaking. Spin wave theory.

  • A is for Annihilation

    Product states and occupation numbers. Creation and annihilation operators. The case of fermions. Representation of operators.

  • B is for Bunching

    Density correlations. Hanbury Brown and Twiss effect. Hartree–Fock theory.

  • Lattice Models

    Tight binding models. Hubbard models and the Mott transition. Superexchange.

  • Bose Gas

    Gross–Pitaevskii approximation. Superfluidity. Bogoliubov theory.

  • Fermi Gas

    Interactions described by perturbation theory. Quasiparticles. Landau Fermi liquid.

  • Superconductivity

    Cooper’s problem. BCS theory. The BCS-BEC crossover.

  • Response and Correlation

    Response functions. Structure factor. Dielectric function. Sum rules.

Course materials

Some books that you may find useful

Past exam papers (with solutions)








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