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Generalized Hydrodynamics is a recent theory that describes the large scaletransport properties of one dimensional integrable models. At the heart of thistheory lies an exact quantum-classical correspondence, which states that theflows of the conserved quantities are essentially quasi-classical even in theinteracting quantum many body models. We provide the algebraic background tothis observation, by embedding the current operators of the integrable spinchains into the canonical framework of Yang-Baxter integrability. Ourconstruction can be applied in a large variety of models including the XXZ spinchains, the Hubbard model, and even in models lacking particle conservationsuch as the XYZ chain. Regarding the XXZ chain we present a simplified proof ofthe recent exact results for the current mean values, and explain how theirquasi-classical nature emerges from the exact computations.

Algebraic construction of current operators in integrable spin chains