Role of Plaquette Term in Genuine 2+1D String Dynamics on Quantum Simulators

With the advent of quantum simulators of 2+1D lattice gauge theories (LGTs), a fundamental open question is under what circumstances the observed physics is genuinely 2+1D rather than effectively 1+1D. Here, we address this question in the ongoing strong effort to quantum-simulate string dynamics in 2+1D LGTs on state-of-the-art quantum hardware. Through tensor network simulations and analytic derivations, we show that the plaquette term, which represents a magnetic field and only emerges in d>1 spatial dimensions, plays a crucial role in genuine 2+1D string dynamics deep in the confined regime. In its absence and for minimal-length (Manhattan-distance) strings, we demonstrate how string breaking, although on a lattice in d=2 spatial dimensions, can be effectively mapped to a 1+1D dynamical process independently of lattice geometry. Our findings not only answer the question of what qualifies as genuine 2+1D string dynamics, but also serve as a clear guide for future quantum simulation experiments of 2+1D LGTs.