Emergent universal quench dynamics in randomly interacting spin models

Universal behaviour often emerges in the low-energy equilibrium physics of quantum many-body systems, despite their microscopic differences. Recently, there has been a growing interest in studying the far-from-equilibrium dynamics of quantum many-body systems. Such dynamics usually involve highly excited states beyond the traditional low-energy theory description. Whether universality can also emerge in such non-equilibrium dynamics is the subject of current research. Here, we report the experimental observation of universal dynamics by monitoring the spin depolarization process in a solid-state nuclear magnetic resonance system, described by an ensemble of randomly interacting spins. The spin depolarization can be related to temporal spin–spin correlation functions at high temperatures. We discover that these correlation functions obey a universal functional form. This finding helps us identify the dominant interacting processes in the spin depolarization dynamics that lead to universality. Our observation demonstrates the existence of universality even in non-equilibrium dynamics at high temperatures, thereby complementing the well-established universality in low-energy physics.