Spin and energy hydrodynamics in low-dimensional materials

Hydrodynamics can be defined as a description of how many-particle systems evolve from local equilibrium to global equilibrium.  An active question in recent years is how electrons might support new kinds of hydrodynamics in very clean materials.  One-dimensional systems often show special behavior because of additional exact or approximate conservation laws, which can be verified by comparison to DMRG-type simulations.  These can even lead to unexpected scaling behavior: we discuss the origin of unusual subdiffusive Kardar-Parisi-Zhang dynamics in the quantum Heisenberg spin-half chain and its recent experimental observation at fairly high temperatures in KCuF3.  Similar behavior was observed with atoms in a quantum gas microscope.  We then explain how even generic (non-integrable) metals in one dimension can show superdiffusive transport because of a competition between Luttinger liquid physics and thermalization.  Some closing comments review other routes to unconventional hydrodynamics in experiment, including in higher dimensions.

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