Observation of Kardar-Parisi-Zhang superdiffusion in a Heisenberg quantum magnet

The Kardar-Parisi-Zhang universality class describes the coarse-grained dynamics of numerous classical stochastic models. Surprisingly, it was recently conjectured, that spin transport in the one-dimensional (1D) quantum Heisenberg model falls into this class. In our experiment, we employ a cold-atom quantum simulator to verify this conjecture by studying the hydrodynamic relaxation of spin-domain walls. We find that transport is superdiffusive and indeed obeys the characteristic KPZ space-time scaling with dynamical exponent z=3/2. We observe that superdiffusion breaks down when probing dynamics both in the 2D model and in the net-magnetized 1D model, which supports the notion that integrability and the non-abelian SU(2) symmetry of the 1D Heisenberg model give rise to its KPZ dynamics. Finally, we leverage the single-spin-sensitive detection enabled by our quantum-gas microscope to measure spin-transport statistics, which yields a clear signature of the non-linearity that is a hallmark of KPZ universality.