From January 22nd to 24th 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)