Lectures provide both the theoretical background and detailed instructions for the computational implementation of the discussed methods. The course is structured into three main parts: the first focuses on atomistic simulations and ion dynamics; the second examines electronic structure and electron-ion interactions using density functional theory; and the third addresses the quantum Monte Carlo description of complex many-body systems.
Part 1: Atomistic Simulations & Ion Dynamics
Hours 1-3: Introduction to computational condensed matter physics. Introduction and setting up atomistic simulations. Modeling bulk materials, surfaces, 2D materials, 1D nanowires, and non-periodic systems (clusters and molecules)
Hours 4-6: Empirical interatomic potentials. Functional forms, parameterisation, and modern highly flexible data-driven potentials. Energy landscapes and structural optimisation.
Hours 7-9: Ion dynamics and Molecular Dynamics (MD) fundamentals. Phase space exploration, statistical ensembles (NVE/NVT/NPT), numerical integrators, and thermostats.
Hours 10-12: Vibrational properties. Phonons, lattice dynamics, free energy, and calculating mechanical and thermal ground-state properties.
Hours 13-14: Bridging scales and advanced ground-state sampling. Coarse-graining. Integrating interatomic potentials into large-scale multiscale workflows and long-time ion dynamics.
Part 2: Electronic Structure Methods - Density Functional Theory
Hours 15-17: Density Functional Theory (DFT) basics. The many-body problem, Born-Oppenheimer approximation, Hohenberg-Kohn theorems, and Kohn-Sham equations. Exchange-correlation functionals.
Hours 18-20: Practical aspects of DFT and electronic structure calculations. Basis sets, pseudopotentials, Brillouin zone sampling, and self-consistent field convergence. Band structure calculations and density of states (DOS). Magnetic properties.
Hours 21-23: Phonons and density functional perturbation theory (DFPT). Short-range and long-range parts of dynamical matrix.
Hours 24-26: Advanced DFT. Electron-phonon coupling. Electronic and lattice transport properties.
Hours 27-28: Advanced electronic and optical properties. Dielectric function within the random phase approximation (RPA) and computational methods in many-body perturbation theory techniques.
Part 3: Quantum Monte Carlo and exact diagonalization
Hours 29-31: Introduction to Monte Carlo methods. Probability theory, Markov chains, and the Metropolis?Hastings algorithm.
Hours 32-34: Variational Monte Carlo I
Hours 35-37: Variational Monte Carlo II
Hours 38-40: Diffusion Monte Carlo and the fermionic sign problem.
Hours 41-42: Exact diagonalization
Final Part: Project Presentations
Hours 43-45: Final project presentations. Discussion of computational implementations and specific problems.
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