Universality classes of spin transport in one-dimensional isotropic magnets: the onset of logarithmic anomalies

Understand

We report a systematic study of finite-temperature spin transport in quantum and classical one-dimensional magnets with isotropic spin interactions, including both integrable and non-integrable models.

• Employing a phenomenological framework based on a generalized Burgers' equation in a time-dependent stochastic environment, we identify four different universality classes of spin fluctuations.
• These comprise, aside from normal spin diffusion, three types of superdiffusive transport: the KPZ universality class and two distinct types of anomalous diffusion with multiplicative logarithmic corrections.
• Our predictions are supported by extensive numerical simulations on various examples of quantum and classical chains.