Quantum many-body physics - from entanglement to emergence

The course covers the following:<br> \- Introduction to problems in quantum many-body physics: emergence and collective behaviour, second quantisation, quantum statistics from second quantisation<br> \- Linear response theory: response functions, classical Drude formula for conductivity, calculations of electromagnetic linear response in quantum physics, f-sum rule<br> \-Spin chains: Jordan-Wigner transformation, XXZ, Heisenberg and Ising models<br> \- Fermi liquid theory: Fermi liquid ground state, quasiparticles and their stability, collective modes, Landau damping, non-Fermi liquids, Green's function and self-energy<br> \- Superfluids and superconductors: physical properties of superfluids and superconductors, BCS theory, spontaneous symmetry breaking and phase stiffness, vortices, the Higgs mechanism in superconductors, boson-vortex duality in two dimensions, chiral superfluids and superconductors<br> \- Quantum spin liquids and fractionalisation: the quantum Ising model, quantum antiferromagnetic order versus resonating-valence-bond state, emergent gauge fields and quantum spin liquids, Ising gauge theory, toric code model, fractionalised excitations and strings, quantum long-range entanglement and topological order<br> \- Numerical methods: tensor networks, neural network quantum states