PhD program Coordinator: 
Alessandro Silva

Students' representative:
Joele Servi

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: 11:00-13:00

Program

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.The last two lectures are "bonus" lectures whose topic and schedule can be arranged during the course, and they can be replaced based on requests. 

7/10/2026A brief reminder of second quantization
12/10/2026Choice of the basis in second quantization. Lattice and continuum modeling
14/10/2026The Hubbard model. Derivation and simple limits
19/10/2026Weak and strong coupling limits of the Hubbard model
21/10/2026Strong-coupling expansion and the tJ model
26/10/2026Hartree-Fock Approximation
04/11/2026HF for the Hubbard model. Finite-temperature Hartree-Fock method
09/11/2026Linear Response Theory
11/11/2026A nice trick: mapping repulsive and attractive Hubbard models
16/11/2026The mean-field theory for the attractive model and how superconductivity emerges
18/11/2026 Superconductivity: some history
TBAWrapping up: The phase diagram of two Hubbard models from simple methods
TBASuperconductivity: beyond BCS (at least in some directions)
TBASuperconductivity and Magnetism, some snapshots of a long movie