Here are some notes on topics that interest me. They will cover numerical methods, interesting physics problems, and reading notes on papers that strongly caught my attention.
The purpose of these notes is not for proposing anything new, but rather for providing detailed derivations, which I believe will be helpful for understanding.
I would be grateful for any feedback and comments about the notes!
The most canonical way of studying an interacting quantum many-body fermion system is simply writing the Hamiltonian as a matrix under suitable basis.
Variational Monte Carlo (VMC) method is a useful numerical technique to evaluate and optimize complicated Ansatz wave functions, which is also very useful in the study of neural quantum states recently.
Translation symmetry and filling constraint guarantees the ground state wave functions in most common condensed matter systems are highly entangled in terms of entanglement depth, which is also interestingly related to the parity super-selection rule (P-SSR) in many-body fermionic systems.
An interesting definite integral problem using Bessel function and residue theorem.
Another interesting definite integral problem, which has some practical usage in the Wannierization for 2D Bloch states.
And this is why Landau levels are inherently "Chern bands".
I don't think I am the only one who got confused by the "normal order" procedure in projected interacting Hamiltonian...
Work in progress ...
under construction ...