Quantum Many Body Systems and Strongly Correlated Electrons

Basic course given by Massimo Capone, Michele Fabrizio

Term: 1

Start: 09-10-2017 End: 21-12-2017 Room: 131

Credits: 6

Schedule: Mon 8:30 - 11:00, Thu 8:30 - 11:00


The basic course will present two cornerstone models of many-body physics: The Hubbard model and the Kondo model. We will use this model to introduce essential tools for many-body physics ranging from linear-response theory to Feynman diagrams.

Here follows the list of lectures. No lectures are scheduled on the week starting October 16 and on November 19, but a lecture is scheduled for Friday, 20.


09/10 A brief reminder of second quantization
12/10 The Hubbard model. Derivation and simple limits
20/10* Linear Response theory. Application to antiferromagnetism in the Hubbard model
26/10 The Hartree-Fock approximation
6/11 Hartree-Fock and the antiferromagnetic phase of the Hubbard model
9/11 Hubbard model in the strong coupling limit. The Heisenberg and t-J models
10/11* Spin-wave theory
13/11 A brief reminder of Superconductivity
16/11 Particle-hole transformation: mapping repulsive and attractive Hubbard model
23/11 Introduction to the Kondo effect
27/11 Feynman diagrams in the Matsubara formalism I.
30/11 Feynman diagrams in the Matsubara formalism II.
4/12 Feynman diagrams in the Matsubara formalism III.
7/12 The resonant level model and scattering theory
The Anderson impurity model and the Hartree-Fock emergence of local moments
14/12 The Kondo model and its log-singularities
18/12 Poor man's scaling
21/12 Local Fermi liquid theory


Online resources

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