From January 22^{nd} to 24^{th} the NRG School participants will be introduced to fundamental aspects of many-body physics to prepare them to follow the lectures by Prof. Žitko. These are the topics to be covered:

**22/01 (09:00 AM to noon): Specific computational tools needed to follow the NRG course (Prof. Gerson Ferreira)**

- Basics of Mathematica syntax
- Data smoothing
- What is the GNU Scientific Library (GSL) and why does it matter?
- What is multiple precision arithmetics and why does it matter? Introducing the GNU Multiple Precision (GMP) Arithmetic Library
- Miscellaneous: Gnuplot, matplotlib, and scripts to manipulate files
- Python and NumPy

**22/01 (2:00 PM to 5:00 PM) A Primer on Many-body Physics (Profa. Mariana Odashima)**

- First and second quantization
- Getting familiar with second quantization
- Some model Hamiltonians in second quantization

**23/01 (09:00 AM to noon) Basics of Green’s functions formalism (Prof. Fabrício de Souza)**

- A few examples of why many-body systems are “different” and why they must be treated by approximate methods
- Green´s functions in many-body physics: what are they and why use them?
- Kramers-Kronig and Hilbert transformations, from real to imaginary

**23/01 (2:00 PM to 5:00 PM) Kondo Physics: Basic Ideas (Prof. George Martins)**

- A short history about the Kondo problem and many-body concepts: the minimum in the resistivity of some metals, Kondo’s calculations and divergencies
- Local moment formation in metals
- Anderson’s Poor man’s scaling and the genesis of renormalization ideas
- The spread of RG ideas to other areas in Physics (from high energy physics to financial markets)

**24/01 (09:00 AM to noon) Introduction to the Kondo and Anderson models (Prof. Edson Vernek)**

- The Kondo model
- The Anderson model
- Gram-Schmidt transformation from the “stat” basis to the Wilson chain basis in the NRG

**24/01 (2:00 PM to 5:00 PM) Kenneth Wilson and the NRG: A Nobel Prize worthy idea (Prof. Edson Vernek)**

- Kenneth Wilson and the development of the Numerical Renormalization Group method
- Closing Remarks

The format of this preparatory course will be traditional lectures both in the morning (from 09:00AM to noon) and in the afternoon (from 2:00PM to 5:00PM). There will be two 15-minute coffee breaks (at 10:30 AM and 3:30PM).

The following text books and review articles will be useful:

- Piers Coleman – Introduction to Many-Body Physics – Cambridge Univ. Press
- Bruus and Flensberg – Many-Body Quantum Theory in Condensed Matter Physics: An Introduction (Oxford Graduate Texts)
- Richard D. Mattuck – A Guide to Feynman Diagrams in the Many-Body Problem: Second Edition – Dover
- Abrikosov/Gorkov/Dzyaloshinski – Methods of Quantum Field Theory in Statistical Physics – Dover
- Fetter and Walecka – Quantum Theory of many-particle systems – Dover
- Wolfgang Nolting – Fundamentals of Many-body Physics – Springer
- Alex C. Hewson – The Kondo Problem to Heavy Fermions – Cambridge University Press
- Philip Phillips – Advanced Solid State Physics – Cambridge University Press
- R. Bulla
*et al.*“Numerical renormalization group method for quantum impurity systems” Rev. Mod. Phys. 80, 395 (2008) - K. G. Wilson “The Renormalization Group and Quantum Phenomena” Rev. Mod. Phys. 55, 583 (1983)
- K. G. Wilson “Renormalization Group – Critical Phenomena and Kondo problem” Rev. Mod. Phys. 47, 773 (1983)
- H. R. Krishna-murthy
*et al.*“Renormalization-group approach to the Anderson model of dilute magnetic alloys. I. Static properties for the symmetric case” Phys. Rev. B 21, 1003 (1980)