This is the website for 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 course has also a follow-up which develops more deeply the theory of strongly correlated electron system and its relation with high-Tc superconductivity.
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.
Here follows the list of lectures. The last two lectures are "bonus" lectures to be agreed on with the students during the course
|3/10/2023||A brief reminder of second quantization|
|4/10/2023||The Hubbard model. Derivation and simple limits|
|10/10/2023||Weak and strong coupling limits of the Hubbard model|
|11/10/2023||Strong-coupling expansion and the tJ model|
|17/10/2023||Spin-waves for the Heisenberg model|
|25/10/2023||Finite-temperature Hartree-Fock method|
|7/11/2023||A nice and useful trick: mapping repulsive and attractive Hubbard models|
|8/11/2023||Superconductivity. BCS theory as a mean-field|
|14/11/2023||The phase diagram of the Hubbard model from simple methods I|
|15/11/2023||The phase diagram of the Hubbard model from simple methods II|
|TBD||Bonus lecture 1|
|TBD||Bonus lecture 2|