Confinement in doped Z2 lattice gauge theories

In proof-of-principle experiments, ultracold atoms have demonstrated that Z2 lattice gauge theories with dynamical matter can be studied in quantum simulators, and realistic proposals for large-scale realizations exist. Motivated by these developments, here we study the deconfinement of U(1) charges in such models, with a strong focus on observables directly accessible from snapshots generated by quantum simulators. We demonstrate that in the τ^x-basis the confined phase is characterized by localized hole pairs connected by (short) strings while deconfinement implies a global net of strings spanning over the entire lattice: We probe deconfinement with Monte Carlo simulations using percolation-inspired order parameters.

Moreover, we simulate a Hamiltonian in two dimensions that is designed from scratch to be experimentally realistic in Rydberg atom array experiments. We show that for small doping, there is a thermal deconfinement phase transition. For large doping, charges are always confined in the thermodynamic limit. For a related three-dimensional model, a thermal deconfinement phase transition exists for arbitrary doping. We map out the phase diagram and calculate the critical exponents. We speculate whether the use of percolation-inspired order parameters can be extended to the Fradkin-Shenker model and related models.