Gauge fields coupled to dynamical matter are a universal framework in many disciplines of physics, ranging from particle to condensed matter physics, but remain poorly understood at strong couplings. Through the steadily increasing control over numerically inaccessible Hilbert spaces, analog quantum simulation platforms have become a powerful tool to study interacting quantum manybody systems. Here we propose a scheme in which a Z2 gauge structure emerges from local two-body interactions and one-body terms in two spatial dimensions. The scheme is suitable for Rydberg atom arrays and enables the experimental study of both (2 + 1)D Z2 lattice gauge theories coupled to dynamical matter (Z2 mLGTs) and quantum dimer models on the honeycomb lattice, for which we derive effective Hamiltonians. We discuss ground-state phase diagrams of the experimentally relevant effective Z2 mLGT for U (1) and quantum-Z2 matter featuring deconfined phases. Further, we present realistic experimental probes and show signatures of disorder-free localization as well as the Schwinger effect in (2 + 1)D using small-scale exact diagonalization studies. Our proposed scheme allows to experimentally study not only longstanding goals of theoretical physics, such as Fradkin and Shenker's [1] conjectured phase diagram, but also go beyond regimes accessible with current numerical techniques.

Gauge fields coupled to dynamical matter are ubiquitous in many disciplines of physics, ranging from particle to condensed matter physics, but their implementation in large-scale quantum simulators remains challenging. Here we propose a realistic scheme for Rydberg atom array experiments in which a $${{\mathbb{Z}}}_{2}$$ Z 2 gauge structure with dynamical charges emerges on experimentally relevant timescales from only local two-body interactions and one-body terms in two spatial dimensions. The scheme enables the experimental study of a variety of models, including (2 + 1)D $${{\mathbb{Z}}}_{2}$$ Z 2 lattice gauge theories coupled to different types of dynamical matter and quantum dimer models on the honeycomb lattice, for which we derive effective Hamiltonians. We discuss ground-state phase diagrams of the experimentally most relevant effective $${{\mathbb{Z}}}_{2}$$ Z 2 lattice gauge theories with dynamical matter featuring various confined and deconfined, quantum spin liquid phases. Further, we present selected probes with immediate experimental relevance, including signatures of disorder-free localization and a thermal deconfinement transition of two charges.