Quantum simulation of Hubbard models: From superconductivity, stripes and pseudogap to lattice gauge theories

Recent advances in quantum gas microscopy, including the achievement of ultra-low temperatures, allow for unprecedented microscopic studies of strongly correlated quantum matter. This talk will focus on Fermi Hubbard models in the strongly interacting regime, which are believed to enable the realization of various exotic states of quantum matter. First I will show how superconductivity can be readily realized and detected in mixed-dimensional fermionic bilayers. Second, applying similar tricks further allows to realize robust stripes in mixed-dimensional monolayers, which have already been seen experimentally. Third, I will discuss a possible scenario of the pseudogap phase found in the Fermi-Hubbard model. It is based on spatially fluctuating stripes, realizing a state with hidden symmetry breaking, and can be directly detected using multi-point correlation functions available to quantum gas microscopy experiments. As an outlook, I will discuss connections to d-wave superconductivity in the Hubbard model with further-neighbor hopping, believed to describe high-Tc cuprate compounds.