Would you be surprised to learn that growing wildfires are described by the same dynamical equations as snow falling and clumping together? Many systems that have different detailed dynamics behave similarly when viewed from a distance. For example, if you have a tub of cold water and you pour a cup of hot water into it, the heat will diffuse and equilibrate in a way that is largely insensitive to the microscopic details of water molecules. Over the last several decades, condensed matter physics has made great progress in classifying physical systems into universality classes with these sorts of common scaling behaviors.
The Kardar-Parisi-Zhang (KPZ) universality class, introduced in 1985 by its namesakes, describes the macroscopic behavior common to a variety of randomly growing interfaces, such as the examples of wildfires and snow accumulating mentioned above. Until recently, all systems in the KPZ universality class were thought to be classical and stochastic. Thus, the Heisenberg model, introduced by Werner Heisenberg in 1928 as a simplified model of interacting quantum magnets, e.g., quantum nuclei, was expected to be very different from typical systems in the KPZ universality class, since it is a quantum model with no randomness in the dynamics.
Surprisingly, however, in 2019, researchers at the University of Ljubljana in Slovenia found a striking resemblance between the way magnetization diffuses in a 1D spin-½ Heisenberg chain (quantum magnets arranged in a line, as displayed below) at infinite temperature and the mathematical predictions of KPZ universality. Their study, which was based on numerical simulations of the Heisenberg model, prompted several experimental groups to further test the conjecture that the Heisenberg model is in the KPZ universality class. These studies, including one that was published in Science, all found further evidence to support the conjecture.