Realistic scheme for quantum simulation of $${{\mathbb{Z}}}_{2}$$ Z 2 lattice gauge theories with dynamical matter in (2 + 1)D

Abstract 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.