Experimental observation of a phase transition in the evolution of many-body systems with dipolar interactions

Non-equilibrium dynamics of many-body systems is important in many branches of science, such as condensed matter, quantum chemistry, and ultracold atoms. Here we report the experimental observation of a phase transition of the quantum coherent dynamics of a 3D many-spin system with dipolar interactions, and determine its critical exponents. Using nuclear magnetic resonance (NMR) on a solid-state system of spins at room-temperature, we quench the interaction Hamiltonian to drive the evolution of the system. The resulting dynamics of the system coherence can be localized or extended, depending on the quench strength. Applying a finite-time scaling analysis to the observed time-evolution of the number of correlated spins, we extract the critical exponents v = s = 0.42 around the phase transition separating a localized from a delocalized dynamical regime. These results show clearly that such nuclear-spin based quantum simulations can effectively model the non-equilibrium dynamics of complex many-body systems, such as 3D spin-networks with dipolar interactions.