Realizing Z2 lattice gauge theories coupled to matter

In a recent preprint, we explain how Z2 lattice gauge theories with couplings to a matter field can be implemented in current ultracold atom experiments. We use DMRG simulations to derive the phase diagram in two-leg ladder model, where we reveal various phases. When tuning the ratio of some microscopic tunnel couplings we predict a transition from a disordered phase to an ordered phase dominated by a Z2 magnetic field with gapped vison excitations. We also demonstrate how 2D lattice gauge theories with local symmetries can be implemented.