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
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.