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Condensed Matter Theory
This is an introductory theory course on quantum materials. A beautiful aspect of such many-body systems is the emergence of various quantum phases of matter that are characterized by broken symmetries or by topological properties of their wavefunctions. Often particle-particle interaction plays a crucial role. The goal of the course is to familiarize the students with the basic physics concepts and with the mathematical tools needed to describe interacting systems and those with topological properties. The twelve lectures will be divided into nine core topics and three special topics.
Syllabus
1. Introduction: Non-interacting electron gas, Slater determinant, second quantization
2. Band theory: Bloch theorem, tight binding, symmetry arguments, metals, semi-metals and insulators
3. Topology: Zak phase, Berry curvature, Dirac materials, topological phase transitions
4. Green’s functions: From quantum mechanics to field theory, retarded, advanced and time ordered Green’s functions, Lehmann representation, spectral function and spectroscopy
5. Linear response theory: Interaction picture, Kubo formalism, generalized response functions, response of a non-interacting electron gas
6. Special topic I: Response of an interacting electron system, quantum and classical phase transitions
7. Special topic II: Interaction induced self-energy, concept of a quasi-particle and its mass, weight and lifetime
8. Special topic III: Hubbard model, interaction driven Mott insulator, spin physics from charge physics
Prerequisites
Evaluation
One homework (20%), a second homework from which selected problems will be asked to solve in class (20%), a final sit-in closed-book exam (60%)