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. The last two lectures are "bonus" lectures whose topic and schedule can be arranged during the course

3/10/2025A brief reminder of second quantization
6/10/2025The Hubbard model. Derivation and simple limits
8/10/2025Weak and strong coupling limits of the Hubbard model
10/10/2025Strong-coupling expansion and the tJ model
20/10/2025Spin-waves for the Heisenberg model
22/10/2025Linear-Response Theory
24/10/2025Hartree-Fock approximation
08/11/2025Finite-temperature Hartree-Fock method
10/11/2025A nice and useful trick: mapping repulsive and attractive Hubbard models
15/11/2025Superconductivity. BCS theory as a mean-field
17/11/2025The phase diagram of the Hubbard model from simple methods I
22/11/2025 The phase diagram of the Hubbard model from simple methods II
TBD Bonus lecture 1
TBD  Bonus lecture 2