Quantum Many Body Systems and Strongly Correlated Electrons I

Basic course given by Massimo Capone, Michele Fabrizio

Term: 1

Start: 07-10-2019 End: 16-12-2019 Room: 131

Credits: 6

Schedule: Mon 8:45 - 11:00, Tue 8:45 - 11:00

Program

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 tentative list of lectures. Additional lectures will be planned during the year.

 

7/10 A brief reminder of second quantization
8/10 The Hubbard model. Derivation and simple limits
14/10 Linear Response theory. Application to antiferromagnetism in the Hubbard model
15/10 The Hartree-Fock approximation
21/10 Hartree-Fock and the antiferromagnetic phase of the Hubbard model
22/10 Hubbard model in the strong coupling limit. The Heisenberg and t-J models
28/10 Spin-wave theory
29/10 A brief reminder of Superconductivity
11/11 Particle-hole transformation: mapping repulsive and attractive Hubbard model
12/11 The basics of Landau Fermi-liquid theory
18/11 Introduction to the Kondo effect
19/11 Feynman diagrams in the Matsubara formalism I.
25/11 Feynman diagrams in the Matsubara formalism II.
26/11 Feynman diagrams in the Matsubara formalism III.

2/12

The resonant level model and scattering theory
3/12
The Anderson impurity model and the Hartree-Fock emergence of local moments
9/12 The Kondo model and its log-singularities
10/12 Poor man's scaling
16/12 Local Fermi liquid theory

Online resources

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