Hydrodynamics in lattice models with continuous non-Abelian symmetries

We develop a systematic effective field theory of hydrodynamics for many-body systems on the lattice with global continuous non-Abelian symmetries. Models symmetries are ubiquitous in physics, arising diverse settings ranging from hot nuclear matter to cold atomic gases and quantum spin chains. In every dimension flavor symmetry group, low energy is set coupled noisy diffusion equations. Independence physics choice canonical or microcanonical ensemble manifest our hydrodynamic expansion, even though causes an apparent shift quasinormal mode spectra. use formalism explain why qualitatively different other conservation laws, including angular momentum charge multipoles. As significant application framework, we study classical one-dimensional SU(2)-invariant chains, Heisenberg model along multiple generalizations. argue based both numerical simulations framework that non-integrable chains exhibit conventional diffusion, contrast some recent predictions constants grow logarithmically at late times. show enhancement due slow equilibration caused by (non-Abelian) fluctuations.