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Last update: Mgr. Kateřina Mikšová (27.12.2023)
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Last update: Mgr. Kateřina Mikšová (27.12.2023)
The completion of the course requires an active participation in solving given problems. During the semester, three computational tasks will be assigned, of which the student must solve one. |
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Last update: Mgr. Kateřina Mikšová (27.12.2023)
During the semester, three computational problems will be assigned, of which the student must solve one to pass the exam. In addition, students must be able to explain the basic concepts of the introduced methods. |
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Last update: Mgr. Kateřina Mikšová (27.12.2023)
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. |