Quantum Many Body Systems and Strongly Correlated Electrons II

Advanced course given by Massimo Capone, Michele Fabrizio

Program

This is the second course of many-body physics. 

The course will explore the effect of interactions in a fermionic system, with a particular emphasis on lattice models (Hubbard models and related). 

The main topics are

- The phase diagram of the Hubbard model: reminder of the antiferromagnetic properties

- a short review of the Landau theory of normal Fermi liquids

- The Gutzwiller approximation

- Slave Particles: Slave Bosons and the Brinkman-Rice transition

- Slave Spins

- (maybe) Hubbard I and III approximations

- Dynamical Mean-Field Theory:

 

• From historical methods to Dynamical Mean-Field Theory: A new view on the correlated electron problem
• How to construct the DMFT: Cavity method
• How to solve DMFT: self-consistency, mapping on impurity models and "impurity" solvers
• The Mott-Hubbard transition in DMFT. Some analytical arguments
• A numerical implementation of DMFT and the Mott transition
• Multiorbital Mott transition: the Hund's coupling, spin-orbit coupling
• Electron-phonon interaction

 

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