Quantum gas microscopes provide experimental access to novel observables, foremost, single particle resolved multi-point correlation functions. These offer a novel microscopic window into the physics of strongly correlated many-body physics.
Building on the work of von Neumann and Wigner, M. Berry showed that there are topologically protected level-crossings in the space of quantum systems. These level-crossings can be detected using the curvature of the Berry connection. In this talk I will describe analogs of this for interacting lattice systems in infinite volume.