U(1) lattice gauge theory and string roughening on a triangular Rydberg array

Lattice gauge theories (LGTs) describe fundamental interactions in particle physics. A central phenomenon in these theories is confinement, which binds quarks and antiquarks into hadrons through the formation of string-like flux tubes of gauge fields. Simulating confinement dynamics is a challenging task, but recent advances in quantum simulation are enabling the exploration of LGTs in regimes beyond the reach of classical computation. For analog devices, a major difficulty is the realization of strong plaquette interactions, which generate string fluctuations that can drive a roughening transition. Understanding string roughening -- where strong transversal functions lead to an effective restoration of translational symmetry at long distances -- is of central importance in the study of confinement. In this work, we show that string roughening emerges naturally in an analog Rydberg quantum simulator. We first map a triangular Rydberg array onto a (2+1)D U(1) LGT where plaquette terms appear as first-order processes. We study flux strings connecting static charges and demonstrate that, near a deconfined quantum critical point, the string exhibits logarithmic growth of its transverse width as the separation between charges increases, along with the universal L\"uscher correction to the confining potential -- both signatures of string roughening. Finally, we investigate the real-time dynamics of an initially rigid string, observing large fluctuations after quenching into the roughening regime, as well as string breaking via particle-pair creation. Our results indicate that rough strings can be realized in experimentally accessible quantum simulators, opening the door to detailed studies of how strong fluctuations influence string-breaking dynamics.