Quantum Many Body Systems and Strongly Correlated Electrons I
Basic Course given by Massimo Capone
Term
1
Credit
4
Start Date
End Date
Room
131
Schedule
Mon: 11:00-13:00
Wed: 9:00-11:00

Program

Updated for Academic Year 2025-2026

This is the  first half of the basic many-body course. The second half is held by Michele Fabrizio right after the end of these lectures.

The basic course introduces some of the main standard tools to study many-particles systems in the concrete case of the Hubbard model and for the study of superconductivity and magnetism. 

The course has also a follow-up -- after the second part of the basic course-- which enters in the more advanced aspects of  the theory of strongly correlated electron system and its relation with high-Tc superconductivity and more recent discoveries.

Here follows the  list of lectures. Note some "deviations" from the standard schedule. The last two lectures are "bonus" lectures whose topic and schedule can be arranged during the course

6/10/2025A brief reminder of second quantization
8/10/2025Choice of the basis in second quantization. Lattice and continuum modeling
10/10/2025The Hubbard model. Derivation and simple limits
13/10/2025Weak and strong coupling limits of the Hubbard model
15/10/2025Strong-coupling expansion and the tJ model
17/10/2025Hartree-Fock Approximation
27/10/2025HF for the Hubbard model. Finite-temperature Hartree-Fock method
28/10/2025A nice trick: mapping repulsive and attractive Hubbard models
3/11/2025Local Holiday
5/11/2025Linear Response Theory
7/11/2025The mean-field theory for the attractive model and how superconductivity emerges
10/11/2025 Superconductivity: some history
12/11/2025Superconductivity: beyond BCS (at least in some directions)
14/11/2025Wrapping up: The phase diagram of two Hubbard models from simple methods