Deep Learning Quantum Physics of Many-Body Systems
Welcome to FGF, „Freie Gemeinde der Fysiker“, a free community of ambitious young physicists who insist on in-depth learning of concepts and methods and strive for a better understanding of physics, in particular, many-body quantum theory of condensed matter.
We aspire to be a democratic, open and progressive community, despite the current trend in academia. It is hard to overemphasise the importance of such a community in current-day situation.
We are going to start a long but joyful journey by studying some pedagogic material on theoretical condensed matter. Every colleague is expected to derive and prove main expressions or results in order to foster an intuitive understanding of them, instead of just learning the buzzwords and browsing away.
Here, we emphasise on the 70s-style pencil-&-paper approach even to solve equations and plot functions (bad for the computer-addicted) [see e.g., Shilov, G. E. “Plotting Graphs”. Mir Publishers (1978)].
It is assumed that the members have an initial working understanding of quantum theory, many-body physics, and approximation techniques, like mean-field theory, or perturbative methods. However, there is no worry if one is still insecure in such matters — community help will be available.
In this community, skepticism is free of charge, and hot in-depth discussions are indeed encouraged, with the proviso that etiquettes of discussion be observed. We will follow the established codes of conduct of
physics.stackexchange. A platform similar to
physics.stackexchange is the ideal where one can discuss matters in depth and with quality, plus anonymity, with credits being awarded for the efforts -- but so far such a platform is not available. Note that in all discussions/correspondences, anonymity must be respected.
The study material will be selected upon community suggestion, but for the initial phase, I’ll suggest some material to begin with, based upon my experience in the field. Note that references should be available in digital form for the members.
On our path, new references will be introduced as we go onwards. Each section will have a paradigmatic problem; for instance, Fermi liquids, Bose-Einstein condensates, superfluid-Mott transition (Bose-Hubbard model), Fermi-Hubbard model, Kondo problem, etc.
It is important to emphasise that we strive for sound mathematics since bad or sloppy mathematics can easily ruin theoretical constructs -- although we may not achieve true mathematical rigour. So we will not shy away from relevant mathematics whenever necessary. “Physics and mathematics are two different sciences and one can fully justify that a physicist’s presentation does not take into account a perfect mathematical rigor even if the author completely masters this one. In physics, it probably is an art to use a minimum of mathematics while remaining precise enough in ones reasoning and presentation that a mathematical physicist can complete all technical details without ambiguities and thereby establish the results and their domain of validity in an irrefutable manner.” [quant-ph/9907069]
You can invite your interested friends to the community, provided they accept the community rules.
It would indeed be remarkable if nature fortified herself against further advances in knowledge, behind the analytical difficulties of the many-body problem.
— Max Born, The Classical Mechanics of the Atom (1960)
See the overall plan of the course here.
See the main references of the course here.
Our own discussion platform.