Condensed matter from a many-electron point of view

Description of the behavior of electrons in matter constitutes a big part of condensed matter and solid state theory.
Non-relativistic quantum mechanics, Pauli principle, and Coulomb interaction are enough to formulate a microscopic theory, and ab-initio approaches based on approximate solutions to the many-electron problem have been well established in material science.
However, most of practical descriptions are based on mappings to effectively non-interacting electrons, approximately including Coulomb interactions either phenomenologically (mean-field like) or adding them perturbatively, sometimes both. Despite their enourmous success
in describing and predicting material properties compared to experiment, theoretical justification is less obvious.
In this course, I will briefly introduce numerical and analytical methods which aim to solve the fulll underlying microscopic (electronic) Hamiltonian, or provide a systematic analysis based on quantum field theoretical methods. I will then discuss from a many-body perspective how the common basic description of electrons in matter emerges in terms of non-interacting quasi-particles in normal Fermi liquids or electrons and holes interacting via screened Coulomb interaction in semiconductors.

• Numerical approaches: Quantum Monte Carlo methods
• Analytical methods: Green'€™s functions, perturbation theory, diagrams
• Many-Fermion wave functions (electron gas)
• From finite to infinite matter: thermodynamic limit considerations
• Born-Oppenheimer approximation, nuclear motion, phonons, band-structure
• Insulator and semiconductors: do electrons interact via bare or screened Coulomb potential?
• Normal Fermi liquids, Luttinger'€™s theorem
• ...