Quantum Theory of Condensed Matter MT 2007

A: Second Quantization
1. Systems of many bosons or fermions
2. Fock Space
3. Tight-binding model

B: Mott Insulators
1. The Hubbard Model
2. Mott transition
3. Heisenberg antiferromagnets

C: Magnetic Insulators
1. Heisenberg Model
2. Holstein-Primakoff representation of spin operators
3. Ferromagnet in the ordered phase
4. Antiferromagnet in the ordered phase
5. Spin-1/2 Heisenberg Chain

D: Superfluidity in systems of weakly interacting bosons
1. Bogoliubov approximation
2. Depletion of the condensate
3. Bogoliubov excitation spectrum

E: Fermi Liquid Theory
1. Adiabatic continuity; quasiparticles
2. Expansion of the free energy; Landau parameters
3. Compressibility and magnetic susceptibility of a Fermi liquid
4. Finite Temperature

F: BCS Theory of Superconductivity
1. Electron-phonon interaction
2. Cooper instability
3. BCS wave function, gap equation.
4. Operator formalism
5. Bogoliubov quasiparticles
6. Temperature dependence of the gap