. "Quantum Physics And Technology"@en . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "Strongly correlated quantum systems"@en . . "6" . "1 Introduction: second quantisation, interacting electrons, the Hubbard model and itsdescendants\n2 Quantum Ising model in transverse magnetic field: exact solution via Jordan Wigner, Fourier and Bogoliubov transform. Quantum phase transitions and criticality. Order an disorder. Duality. Excitations and domain walls. Entanglement entropy: area laws and logarithmic divergence.\n3 Half-integer spin chains: Heisenberg antiferromagnets, Lieb-Schultz-Mattis theorem, order and disorder, Goldstone-bosons, Mermin-Wagner theorem, exact solution via coordinate Bethe ansatz.\n4 Integer spin chains: Haldane’s conjecture, Affleck-Kennedy-Tasaki-Lieb model, introduction to MPS (Matrix Product States) and tensor networks. Gapless edge modes and symmetry protected topological order.\n5 Topological classification of free fermion systems: periodic table of topological insulators and superconductors, Su-Schriefer-Heeger model and Kitaev’s quantum wire: topological.\ndegeneracy and majorana edge modes.\r\n6 Spin models in higher dimensions, spin liquids, gauge theories and Kitaev's toric code\r\n1 model, topological order and anyons\r\nThere will also be a group project, which can be chosen as either a literature review (e.g.\r\nquantum hall effect, Levin-Wen string net models, topological insulators, entanglement\r\nrenormalization for critical systems, entanglement entropy in conformal field theory, …) or\r\n(density matrix renormalization group algorithm, tensor renormalization group, …)." . . "Presential"@en . "FALSE" . . "Master of Science in Physics and Astronomy"@en . . "https://images.communicate.vub.ac.be/Web/VUB/%7Be03fbc44-87f1-488a-badd-e287777c0353%7D_WE_oplBrochure_MB_EN_Physics-Astronomy_8P.pdf?utm_medium=email&utm_source=eloqua&utm_content=MARCOM%20REKRUTERING%20brochure%20download%20ENG&%3Cutm_campaign= https://www.vub.be/en/studying-vub/all-study-programmes-vub/bachelors-and-masters-programmes-vub/master-in-physics-and-astronomy/program/master/master-physics-and-astronomy-minor-research\n" . "120"^^ . "Presential"@en . "The Master of Science in Physics and Astronomy: Minor Research is composed of 30 ECTS compulsory courses, 30 ECTS master thesis, 10-12 ECTS external mobility courses and 48-50 ECTS minor Research Electives. Our Master is jointly organized with UGent.\n\nPhysics aims at understanding the world around us by observing it from the smallest scales to the scale of the universe itself. From those observations, models are built to allow us to understand, explain and eventually predict the behavior of nature. The Master in Physics and Astronomy provides a comprehensive education in physics covering the particle physics, general relativity, astrophysics and the study of complex systems.\n\nThis master will give you quantitative and analytic skills that are useful to solve many problems arising in many areas beyond physics."@en . . . "2"@en . "TRUE" . . "Master"@en . "Thesis" . "1092.10" . "Euro"@en . "3620.00" . "Recommended" . "As a physicist you will be in high demand on the job market. With a master in Physics and Astronomy from VUB, you will have the knowledge and skills to land a job in one of many diverse sectors.\n\nThere is plenty of work in scientific research at universities and research institutes. In industry, in modelling, statistics and informatics. Alternatively, work on risk analysis and modelling in the banking, finance or pharmaceuticals sectors. You will also be valuable in the field of education. Infinite opportunities, in fact!"@en . "2"^^ . "TRUE" . "Upstream"@en . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .