From January 25th to February 31st, Prof. Žitko will present the topics listed below.

Prof. Žitko’s lectures are available here:


01/25/2019 (9:00 AM to noon) – Lecture Topics

  • quantum impurities, historical background, quantum dots, magnetic adsorbates, applications in the DMFT
  • Anderson model, equations of motion, hybridization function, self-energy, Schrieffer-Wolff transformation to Kondo model
  • thermodynamics of the Anderson model, Kondo resonance

01/25/2019 (2:00 PM to 5:00 PM) – Mathematica training session

    Mr. Daniel de Souza Carvalho, a certified Mathematica instructor, will deliver a Mathematica training session to the NRG UFU/2019 participants.

01/26/2019 (9:00 AM to noon) – Homework

  • analytical properties of Green’s functions and self-energy functions
  • Hilbert transformation, Kramers-Kronig transformation, evaluation of hybridization
    functions for common densities of states
  • exact solution of the resonant-level model

01/28/2019 (9:00 AM to noon) – Lecture Topics

  • mapping of an impurity model to a one-dimensional problem, discretization, Gram-Schmidt tri-diagonalization
  • NRG iteration, property of energy-scale separation, truncation of states, systematic errors
  • elementary notions of RG paradigm: fixed points, operator content, scaling, exponents

01/28/2019 (2:00 PM to 5:00 PM) – Homework and Computer Lab

  • 2nd order perturbation-theory and Hartree-Fock solution of the Anderson impurity model
  • zero bandwidth limit of the Anderson impurity model
  • NRG calculation of RG flows, expectation values and thermodynamic properties

01/29/2019 (9:00 AM to noon) – Lecture Topics

  • calculation of dynamical properties, spectral representation, broadening
  • technical tricks: efficient truncation, z-averaging, large-Lambda calculations, symmetries, suppression of floating-point errors
  • density-matrix calculation, complete Fock space construction, DMNRG, CFSNRG and FDMNRG algorithms for dynamical properties

01/29/2019 (2:00 PM to 5:00 PM) – Homework and Computer Lab

  • calculation of spectral function of AIM using different algorithms
  • error trade-offs: truncation vs. discretization, choice of Lambda
  • charge and spin susceptibilities

01/30/2019 (9:00 AM to noon) – Lecture Topics

  • details of discretization schemes, systematic errors and their suppression
  • the self-energy trick for Anderson impurity model and Kondo model
  • multi-orbital problems: discretization issues, handling big problems, parallelization issues

01/30/2019 (2:00 PM to 5:00 PM) – Homework and Computer Lab

  • handling arbitrary DOS (energy-dependent hybridization functions), pseudo-gap DOS, diverging DOS, gaps
  • calculation of high-resolution spectral functions
  • scaling of CPU and memory requirements

02/31/2019 (9:00 AM to noon) – Lecture Topics

  • external magnetic field on the impurity and in the continuum, compensation theorems
  • AIM with superconducting continuum, Yu-Shiba-Rusinov states

02/31/2019 (2:00 PM to 5:00 PM) – Homework and Computer Lab

  • Zeeman splitting of the Kondo resonance
  • calculation of anomalous spectral functions
  • sub-gap spectra and Yu-Shiba-Rusinov states