Syllabus
NRG: 1. Spin one half immersed in the band of electrons: introduction to (s-d) Kondo and
Anderson models, their nonperturbative Renormalization Group (RG) solution. 2. Scaling and RG flow for (s-d) Kondo and Anderson models: NRG Ljubljana implementation. 3. Practical aspects of running NRG Ljubljana and other NRG codes for various problems. 4. Superconducting Anderson model for quantum computation devices: current developments in NRG (qubits, Bohm-Aharonov rings, topological systems).
Tensor Networks and DMRG: 1. Practical introduction to Tensor Networks: Matrix Product States (MPS) and Projected
Entangled Pair States (PEPS). 2. Density Matrix Renormalization Group (DMRG) algorithm step by step. 3. ITensor: crash course in Julia, setting a simple calculation. 4. Simple systems: spins (1D and 2D Heisenberg model), fermions (tJ model), qubits.
Green functions and QMC: 1. Practical introduction to many-body Green functions. 2. Effects of electron interactions: Anderson impurity and Hubbard models - the basics. 3. Introduction to Monte Carlo methods. 4. Hybridization-expansion QMC - the basic description of the algorithm and simple calculations using the TRIQS package. 5. Analytic continuation of imaginary-time QMC data as an example of an ill-defined problem in physics.
Annotation
The aim of the course is to offer a pragmatic introduction into the state-of-the art computational methods in condensed matter theory. Emphasis is placed on three techniques: numerical renormalization group (NRG), density matrix renormalization group (DMRG), and quantum
Monte Carlo (QMC). These methods play a crucial role in development of quantum computation circuits, material engineering, nanotechnology and related disciplines. The course lays down theoretical foundations for each method and then offers hands-on exploration of some of their well-established numerical implementations.