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We study variable-rate linear quenches in the anisotropic Heisenberg (XXZ)chain, starting at the XX point. This is equivalent to switching on a nearestneighbour interaction for hard-core bosons or an interaction quench for freefermions. The physical observables we investigate are: the energy pumped intothe system during the quench, the spin-flip correlation function, and thebipartite fluctuations of the z component of the spin in a box. We findexcellent agreement between exact numerics (infinite system time-evolving blockdecimation, iTEBD) and analytical results from bosonization, as a function ofthe quench time, spatial coordinate and interaction strength. This provides astringent and much-needed test of Luttinger liquid theory in a non-equilibriumsituation.

Linear quantum quench in the Heisenberg XXZ chain: time dependent Luttinger model description of a lattice system