Realistic scheme for quantum simulation of $\mathbb{Z}_2$ lattice gauge theories with dynamical matter in $(2+1)$D

Understand

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 $\mathbb{Z}_2$ 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 $\mathbb{Z}_2$ 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 $\mathbb{Z}_2$ lattice gauge theories with dynamical matter featuring various confined and deconfined, quantum spin liquid phases.