Partial confinement in a quantum-link simulator

Confinement and deconfinement, captivating attributes of high-energy elementary particles, have recently garnered wide attention in quantum simulations based on cold atoms. However, partial confinement, an intermediate state between the confinement and deconfinement, remains underexplored. The partial confinement encapsulates the phenomenon that the confining behavior of charged particles is contingent upon their relative positions. In this paper we demonstrate that the spin-1 quantum-link model provides an excellent platform for exploring partial confinement. We conduct a comprehensive investigation of the physics emerging from partial confinement in the context of both equilibrium and nonequilibrium dynamics. Potential experimental setups using cold atoms are also discussed. Our work offers a simple and feasible routine for the study of confinement-related physics in the state-of-the-art artificial quantum systems subject to gauge symmetries.