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