Quantum matter

The course begins with exact organizing principles, symmetry, conservation laws, and translation invariance, and then develops the theoretical frameworks needed to study systems for which exact solutions are generally unavailable. These include band theory, second quantization, mean-field theory, collective excitations, light-matter coupling, and Green’s functions. The course applies these tools across a broad range of settings, from electrons in crystals and topological chains to quantum gases, superfluids, magnets, photons, and open quantum systems. These examples show how the same concepts and methods recur in different physical contexts.

This is a theory course, centered around constructing and interpolating models. Students are expected to follow mathematical arguments. 

Course aims

• Build a coherent theoretical framework to understand distinct forms of quantum matter.
• Develop fluency in the representations used in modern condensed matter theory: momentum space, band space, Fock space, quasiparticle space, and spectral space.
• Prepare students for advanced courses and research in condensed matter physics, including interacting quantum systems, topology, magnetism, quantum optics, transport, and nonequilibrium physics.