Exotic Bound Hadrons in $\mathbb{Z}_2$ Lattice Gauge Theories

Lattice gauge theories (LGTs) provide a minimal setting to study confinement, bound-state formation, and dynamics relevant to both high-energy and condensed-matter physics, and are now accessible in programmable quantum simulators. We first describe how 1+1D $\mathbb{Z}_2$ LGT supports repulsively bound hadronic states: stable four-particle bound states that energetically lie above a two-meson continuum [arXiv:2510.23618]. We extend this to two dimensions and explore bound-state formation driven by magnetic plaquette terms. Focusing on $2+1$D $\mathbb{Z}_2$ gauge theory coupled to Ising matter, we identify resonant plaquette states composed of parallel dimers and U-shaped string configurations. We show that magnetic fluctuations can stabilize magnetically bound tetraquark-like states, whose decay into delocalized dimers is suppressed despite available decay channels. Our results raise several questions, including the mobility of these bound states, their stability beyond single plaquettes, and whether generic string configurations preferentially bind via magnetic interactions. These phenomena highlight the richness of emergent hadronic physics in minimal lattice gauge theories and suggest concrete targets for near-term quantum simulation experiments.