Detection of Kardar-Parisi-Zhang Hydrodynamics in a quantum Heisenberg spin-half chain

Classical hydrodynamics is a remarkably versatile description of the coarse-grained behavior of many-particle systems once local equilibrium has been established. The form of the hydrodynamical equations is determined by the conserved quantities present in a system. Generically, there is a small number of conserved quantities, which give rise to diffusive transport properties. However, in integrable systems with an extensive number of conserved quantities, more exotic transport properties are possible. In particular, recent work suggests the spin-half Heisenberg chain exhibits Kardar-Parisi-Zhang (KPZ) dynamics at infinite temperature. In this work, we study the dynamical structure factor using a tensor network approach, and show signatures of KPZ survive at finite temperatures. Moreover, we find excellent agreement with neutron scattering experiments on the compound KCuF3, suggesting KPZ physics is present.