Emerging Gauge Fields caused by Density-Dependent Peierls Phases in Rydberg Arrays

It has been shown experimentally that spin-orbit coupling in systems of Rydberg atoms gives rise to density-dependent Peierls Phases [Lienhard et al., PRX 10, 021031 (2020)] in the hopping process of Rydberg spin excitations. In this work we expand on this and study a one-dimensional zig-zag ladder system of identical spin-orbit coupled Rydberg atoms exhibiting such a density-dependent hopping in addition to a van-der-Waals like repulsion. We show that beyond the mean-field level, the density-dependent hopping generates a dynamical gauge field. In the liquid state, where hopping processes dominate, the emerging gauge field displays liquid-like flux correlations. In the ordered phase, where repulsion dominates, a flux lattice with long-range correlations is formed.