Quantum Theory of Solids by Subir Sachdev

I started Prof. Sachdev’s Havard course Physics 295b: Quantum Theory of Solids in the end of October 2021, and finished the first 30 lecture videos in the beginning of February 2022. For me, this course feels like the ideal next step after learning the usual undergraduate solid state physics course (talking about things like nearly free electron model, tight-bonding model, bond structure, X-ray or neutron scattering experiments…).

Subir Sachdev did an excellent job introducing techniques like

• Second quantization formulation
• Green’s function
• Mean field theory approach to interacting systems
• Diagrammatic perturbation theory

He used these powerful techniques to analyze systems like

• Free and interacting electron gas with a positive charge background (or the Jellium model). In the undergraduate solid state physics, the interesting things arise due to the periodic background potential interacting with the electron, but the interaction between electron them self is ignored. Here, we explore the situation where the background potential is trivial (uniform) but consider the effect of the Coulomb interaction between electrons.
• BSC theory of superconductivity. The key seems to relax the assumption of the ground state wavefunction; it doesn’t have to conserve particle number.
• Hubbard model.
• The Kondo lattice, disordered metals and SYK model (I didn’t go to this far in this course).

The main textbook of this course is Bruus and Flensberg’s book. The second-quantized operator formalism is used exclusively during the course. In this sense, a good companion book might be Atland and Simons’s, using the coherent-state path integration formualism a lot.

What do I learn the most?

I got familiar with the second-quantization formalism and mean-field theory in the operator language by following this course. I’m also amazed to see so many interesting physical phenomena coming out of the interacting of many degrees of freedom and how powerful the techniques like mean-field approximation and the perturbation theory.