Quantum simulating doped quantum magnets with bosonic systems

Following the discovery of high temperature superconductivity, unraveling its origins has become a key problem of condensed matter physics. From a model perspective, a wealth of research has concentrated on the Fermi-Hubbard model, which has been a key motivation for analog quantum simulation using fermionic atoms in optical lattices. In the strong coupling limit, the Hubbard model can be approximated by the t-J model, though numerical predictions for the ground state phase diagram can differ between the two models. In this talk, I will discuss how we can reconcile theoretical results for the t-J and Hubbard model, starting on the level of a single pair, thus motivating the study of t-J models directly. While the fermionic nature of electrons suggests the study of the fermionic t-J model, the interplay of spin and charge degrees of freedom is also captured by its bosonic variant. I will present two different possibilities to realize a bosonic t-J model in quantum simulation experiments: (i) an optical lattice implementation, featuring dynamics in a strong staggered magnetic field, and (ii) an implementation using three Rydberg states in a tweezer array. As an outlook, I will present numerical results for the ground state phase diagram at finite doping.