Green's function, structure factor etc. calculations

[Yue-Zhengyuan]

Does MPSKit currently have (or plan to support) the functionality to calculate Green's function like

$$G(k, \beta/2) = \frac{tr(e^{-\beta H/2} c_{k\sigma} e^{-\beta H/2} c^\dagger_{k\sigma})}{tr(e^{-\beta H})} = \int_{-\infty}^{\infty} \frac{d\omega}{2\pi} \frac{A(k,\omega)}{2\cosh(\beta\omega/2)}$$

[lkdvos]

In principle all the basic tools are there, but we are definitely missing some higher-level functionality for this that shows how to compose the pieces. I will give a shout-out to https://github.com/Quantum-Many-Body/DynamicalCorrelators.jl, which might have a little bit more of the functionality you are looking for.

I would definitely not be opposed to adding some of this to the package here, I just probably won't find the time to do this myself immediately.

[lkdvos]

Also linking this here, since I should finish that work: https://github.com/QuantumKitHub/MPSKit.jl/tree/dynamical/examples/quantum1d/9.dynamical-correlator
This is a WIP example in a separate branch here.