# Quantum many-body physics - from entanglement to emergence

7.5 ECTS creditsThe course covers the following:

- Introduction to problems in quantum many-body physics: emergence and collective behaviour, second quantisation, quantum statistics from second quantisation

- Path integral formulation of quantum many-body problems: single-particle quantum mechanics from the path integral, partition function as a functional integral, coherent states and functional integrals

- Linear response theory: response functions, classical Drude formula for conductivity, calculations of electromagnetic linear response in quantum physics, f-sum rule

- Fermi liquid theory: Fermi liquid ground state, quasiparticles and their stability, collective modes, Landau damping, non-Fermi liquids, Green's function and self-energy

- 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, the Berezinskii-Kosterlitz-Thouless transition, chiral superfluids and superconductors

- 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

- Introduction to problems in quantum many-body physics: emergence and collective behaviour, second quantisation, quantum statistics from second quantisation

- Path integral formulation of quantum many-body problems: single-particle quantum mechanics from the path integral, partition function as a functional integral, coherent states and functional integrals

- Linear response theory: response functions, classical Drude formula for conductivity, calculations of electromagnetic linear response in quantum physics, f-sum rule

- Fermi liquid theory: Fermi liquid ground state, quasiparticles and their stability, collective modes, Landau damping, non-Fermi liquids, Green's function and self-energy

- 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, the Berezinskii-Kosterlitz-Thouless transition, chiral superfluids and superconductors

- 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

Progressive specialisation:
A1F (has second‐cycle course/s as entry requirements)

Education level:
Master's level

Admission requirements:
90 ECTS credits in Physics, including Quantum Physics I, 7.5 ECTS credits, Solid State Physics, 7.5 ECTS credits, and Analytic Mechanics, 7.5 ECTS credits, plus 45 ECTS credits in Mathematics, including Linear Algebra, 7.5 ECTS credits, Calculus and Geometry, 7.5 ECTS credits, and Calculus in Several Variables, 7.5 ECTS credits, and registered for Symmetry - Mathematical Structures and Applications, 7.5 ECTS credits, plus upper secondary level English 6, or equivalent

Selection:

Selection is usually based on your grade point average from upper secondary school or the number of credit points from previous university studies, or both.

### This course is included in the following programme

- Master of Science in Engineering Physics (studied during year 4)