Quantum Many Body Systems and Strongly Correlated Electrons I

Basic course given by Massimo Capone, Michele Fabrizio

Term: 1

Start: 03-10-2018 End: 29-01-2019 Room: 131

Credits: 6

Schedule: Mon 8:30 - 11:00, Tue 11:00 - 13:30


The many-body course is divided into two courses a "main" course for 6 credits and an advanced course for 4 credits (See https://cm.sissa.it/phdsection/descriptioncourse.php?ID=23 )


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 the first lectures. Additional lectures will be planned during the year.


2/10 A brief reminder of second quantization
8/10 The Hubbard model. Derivation and simple limits
9/10 Linear Response theory. Application to antiferromagnetism in the Hubbard model
15/10 The Hartree-Fock approximation
16/10 Hartree-Fock and the antiferromagnetic phase of the Hubbard model
23/10 Hubbard model in the strong coupling limit. The Heisenberg and t-J models
29/10 Spin-wave theory
30/10 A brief reminder of Superconductivity
12/11 Particle-hole transformation: mapping repulsive and attractive Hubbard model
13/11 The basics of Landau Fermi-liquid theory
19/11 Introduction to the Kondo effect
20/11 Feynman diagrams in the Matsubara formalism I.
26/11 Feynman diagrams in the Matsubara formalism II.
27/11 Feynman diagrams in the Matsubara formalism III.
3/12 The resonant level model and scattering theory
The Anderson impurity model and the Hartree-Fock emergence of local moments
10/12 The Kondo model and its log-singularities
11/12 Poor man's scaling
17/12 Local Fermi liquid theory

Online resources

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