Lattice gauge theories (LGTs) were introduced in 1974 by Wilson to study quark confinement. These models have been shown to exhibit (de)confined phases, yet it remains challenging to define experimentally accessible order parameters. Here we propose percolation-inspired order parameters (POPs) to probe confinement of dynamical matter in ${\mathbb{Z}}_2$ LGTs using electric field basis snapshots accessible to quantum simulators. We apply the POPs to study a classical ${\mathbb{Z}}_2$ LGT and find a confining phase up to temperature $T=\infty$ in two dimensions (critical $T_c$, i.e., finite-$T$ phase transition, in three dimensions) for any nonzero density of ${\mathbb{Z}}_2$ charges. Further, using quantum Monte Carlo we demonstrate that the POPs reproduce the square lattice Fradkin-Shenker phase diagram at $T=0$ and explore the phase diagram at $T>0$. The correlation length exponent coincides with the one of the three-dimensional Ising universality class and we determine the POP critical exponent characterizing percolation. Our proposed POPs provide a geometric perspective of confinement and are directly accessible to snapshots obtained in quantum simulators, making them suitable as a probe for quantum spin liquids.

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• Confinement
• Percolation
• Percolation phase transition
• Quantum simulation
• Quantum spin liquid
• Topological order
• Lattice gauge theory
• Quantum Monte Carlo