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`

Interested in theoretical condensed matter research?

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## Lectures

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

### Synopsis

##### 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

- Advanced Quantum Mechanics - A Practical Guide, Nazarov and Danon
- Introduction to Many-Body Physics, Coleman
- Interacting Electrons and Quantum Magnetism, Assa Auerbach

## Past exam papers (with solutions)

## Discuss

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