Welcome to the Part III Physics course
** Theories of Quantum Matter**, running in Michaelmas 2018. The goals and structure of this course
are described here.

There will be four supervisions, each with their own set of problems.

## Important Announcement 1

In this course $\hbar = 1$. Momentum has the units of inverse length; energy has units of inverse time; angular momentum is dimensionless, etc..

## Important Announcement 2

In the text you will see questions contained in boxes like this one. You will be answering these questions in the lecture!

## Outline of Lectures

Product States. Fermi gas. Density, density matrix, and pair distribution.
Landau levels. Laughlin wavefunction. Fractional charge, Fractional statistics.
Quantizing a chain. Ground state displacement fluctuations.
Heisenberg model; Heisenberg chain; Magnons; Antiferromagnets; Symmetry breaking; Spin wave theory.
Product states and occupation numbers. Creation and annihilation operators. The case of fermions. Representation of operators.
Density correlations. Hanbury Brown and Twiss effect. Hartree--Fock theory.
Tight binding models. Hubbard models and the Mott transition. Superexchange.
Gross--Pitaevskii approximation. Superfluidity. Bogoliubov theory.
Interactions described by perturbation theory. Quasiparticles. Landau Fermi liquid.
Cooper's problem. BCS theory. The BCS-BEC crossover.
Response functions. Structure factor. Dielectric function. Sum rules.
Perturbation series for partition function and free energy. Screening.
Spin-1/2 XY model as a system of free fermions. Bosonization.
The Kondo model. Divergences at second order. Scaling theory.
Bethe's wave function. The Bethe equations. Excited states.