Quantum Many Body Systems and Strongly Correlated Electrons I

Basic course given by Massimo Capone

Term: 1

Start: 01-10-2020 End: 18-12-2020 Room: 131

Credits: 3

Schedule: Tue 11:00 - 13:00, Wed 11:00 - 13:00

Program

This is the website for the first half of the "basic" many-body course. 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. One/two extra lecture with applications will be scheduled during the course to meet the students' needs.

 

5/10 A brief reminder of second quantization
6/10 The Hubbard model. Derivation and simple limits
12/10 The Hartree-Fock approximation
13/10 Linear Response theory. Application to antiferromagnetism in the Hubbard model
19/10 Hartree-Fock and the antiferromagnetic phase of the Hubbard model
20/10 Strong-coupling expansion. Theory and the tJ model
26/10 A nice and useful trick: mapping repulsive and attractive Hubbard models
8/11 Superconductivity. BCS theory as a mean-field
9/11 Superconductivity. Beyond BCS with simple tools. BCS/BEC crossover
17/11 The phase diagram of the Hubbard model from simple methods
18/11 Multiorbital Hubbard models (TBD)
   
   
   
   
   
   
   
   

Online resources

Filename Size Date Modified
manybody.pdf 2.36 MB 2017-09-19 15:32:38