Quantum Many Body Systems and Strongly Correlated Electrons
Basic course given by Massimo Capone, Michele Fabrizio
- 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
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