From January 25^{th} to February 31^{st}, Prof. Žitko will present the topics listed below.
Prof. Žitko’s lectures are available here:
 [PDF] A comprehensive (19 pages) description of the topics
 [PDF] Lecture 1
 [PDF] Lecture 2
 [PDF] Lecture 3
 [PDF] Lecture 4
 [PDF] Lecture 5
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, selfenergy, SchriefferWolff 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 selfenergy functions
 Hilbert transformation, KramersKronig transformation, evaluation of hybridization
functions for common densities of states  exact solution of the resonantlevel model
01/28/2019 (9:00 AM to noon) – Lecture Topics
 mapping of an impurity model to a onedimensional problem, discretization, GramSchmidt tridiagonalization
 NRG iteration, property of energyscale 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
 2^{nd} order perturbationtheory and HartreeFock 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, zaveraging, largeLambda calculations, symmetries, suppression of floatingpoint errors
 densitymatrix 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 tradeoffs: 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 selfenergy trick for Anderson impurity model and Kondo model
 multiorbital 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 (energydependent hybridization functions), pseudogap DOS, diverging DOS, gaps
 calculation of highresolution 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, YuShibaRusinov 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
 subgap spectra and YuShibaRusinov states