Long-lived phantom helix states in Heisenberg quantum magnets

Exact solutions for quantum many-body systems are rare but provide valuable insights for the description of universal phenomena such as the non-equilibrium dynamics of strongly interacting systems and the characterization of new forms of quantum matter. Recently, specific solutions of the Bethe ansatz equations for integrable spin models were found. They are dubbed phantom Bethe states and can carry macroscopic momentum yet no energy. Here, we show experimentally that there exist special helical spin patterns in anisotropic Heisenberg chains which are long-lived, relaxing only very slowly in dynamics, as a consequence of such states. We use these phantom spin-helix states to directly measure the interaction anisotropy, which has a major contribution from short-range off-site interactions. We also generalize the theoretical description to higher dimensions and other non-integrable systems and find analogous stable spin helices, which should show non-thermalizing dynamics associated with so-called quantum many-body scars. These results have implications for the quantum simulation of spin physics, as well as many-body dynamics.