Joel Moore - University of California, Berkeley
Wednesday, August 9th, 10:45AM EDT (Zoom meeting starts at 10:30 EDT)
Hydrodynamic limits of integrable and near-integrable spin chains in theory and experiment
The ground states and thermodynamics of simple integrable spin chains such as the XXZ model have been well understood for many years. The past ten years or so have seen remarkable changes in our understanding of their dynamical properties. Using the XXZ model as an example, this talk discusses the emergence of two different hydrodynamic regimes in the gapless, interacting part of the phase diagram. A relatively simple kind of ballistic behavior, familiar from classical integrable PDEs, describes the easy-plane limit, while superdiffusive scaling and KPZ-like properties emerge at the Heisenberg point. We discuss the current understanding of KPZ-like behavior with dynamical critical exponent z=3/2 in integrable models with non-abelian symmetries and its relevance to recent experiments on both the spin chain compound KCuF3 and atomic emulators. The last part of the talk considers two kinds of integrability breaking that are relevant to different kinds of experiments but not yet completely understood. Putting an integrable system in an external trap, as commonly done in atomic experiments, acts to break the integrability but only weakly in some cases. Adding additional interactions on a spin chain, or interactions between chains, often leads to diffusion in linear response but superdiffusion in strongly driven systems.