# Dr. Žiga Krajnik (FMF): Anomalous spin dynamics in one-dimensional magnets

One-dimensional models are a theoretical playground for the investigation of strongly interacting many-body dynamics that in recent years have become experimentally realizable. While mean-field methods and other standard approaches are not applicable to one-dimensional systems, they can be investigated theoretically with techniques of integrability and generalized hydrodynamics. After a brief overview of these methods, we discuss recent surprising observations of anomalous spin dynamics in the XXZ spin chain and its classical analogue at half-filling, with a particular focus on super-diffusive dynamics at the isotropic point. While the dynamical structure factor indicates a connection with the Kardar-Parisi-Zhang universality class, a symmetry argument rules out a simple identification. Investigations of fluctuations reveal further surprises, exhibiting equilibrium dynamical criticality in the easy-axis regime and at the isotropic point. We introduce a toy model of kinetically constrained charged particles whose exact solution matches the anomalous fluctuation phenomenology in the easy-axis regime of the spin chain at equilibrium. Out of equilibrium one generically finds first and second order dynamical phase transitions.

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