Frontiers of quantum simulation: from doped quantum magnets to gauge theories

Twenty five years after the first proposal of quantum simulation in cold atoms, the platform has become a complementary method in the study of strongly-correlated systems. The increasing complexity of accessible models necessitates an even tighter collaboration between theory and experiment to develop realistic schemes and to analyze experimental data. In my talk, I will focus on two schemes for the implementation of doped quantum magnets and lattice gauge theories. The former utilizes three internal molecular or Rydberg states, which allows to realize bosonic antiferromagnetic t-J models in static tweezers arrays. For the latter, I will present a theoretical framework that reduces the complexity of local symmetry generators from four to two-body interactions and enables a large-scale realization of Z2 lattice gauge theories with dynamical matter in Rydberg tweezer arrays beyond 1D, based on the idea of gauge protection. In the last part, I will extend gauge protection to non-Abelian SU(N) gauge theories and show that readily available Hubbard and Heisenberg interactions are sufficient to stabilize SU(N) lattice gauge theories in any dimension.