Our latest work on creating Hubbard Models for Quasicrystalline Potentials is now on the Arxiv (2210.05691).
In it, we present a numerical method for constructing the Hubbard Hamiltonian of non-periodic potentials without making use of Bloch's theorem, and then apply it to the eightfold rotationally symmetric 2D optical quasicrystal we have created in the experiment.
This work will not allow one to construct arbitrarily large tight-binding graphs for numerical many-body calculations, it also enables new analytic arguments on the topological structure and many-body physics of these models.