Quantum Many Body Systems and Strongly Correlated Electrons

Basic course given by Massimo Capone, Michele Fabrizio

Start: 09-10-2017 End: 21-12-2017 Room: 131
Schedule: Mon 8:30 - 11:00, Thu 8:30 - 11:00

Program

  • Second Quantization. Fock Space, canonical transformations
  • Applications: Electrons is a periodic lattice, the Hubbard model
  • Hartree-Fock Approximation at zero temperature
  • Hartree-Fock Approximation at finite temperature
  • Antiferromagnetism in the Hubbard model
  • Strong-coupling limit, the Heisenberg model, the t-J model
  • Superconductivity in the attractive Hubbard model: a unitary transformation and the BCS-BEC crossover
  • Response Functions. Linear Response Theory.
  • Kramers-Kronig Relations. Fluctuation-Dissipation Theorem.
  • Optical Conductivity.
  • Feynmann Diagrams. Perturbation Expansion in Imaginary Time
  • Single particle Green's functions and Feynmann Diagrams
  • The Dyson Equation. Self-energy
  • Two-particle Green's functions and correlation functions
  • The vertex function. Irreducible Vertices and the Bethe-Salpeter Equations
  • Ward Identities and Conservation Laws
  • Landau Theory of Normal Fermi Liquids. The energy functional and quasiparticles
  • Thermodynamic Quantities.
  • Transport. Collective excitations, zero sound, first sound
  • Microscopic basis of Landau Fermi-liquid theory
  • The Mott-Hubbard transition
  • The Gutzwiller method
  • Dynamical Mean-Field theory

Online resources

Filename Size Date Modified
manybody.pdf 2.36 MB 2017-09-19 15:32:38