Integrability-Protected Adiabatic Reversibility in Quantum Spin Chains

We consider the out-of-equilibrium dynamics of the Heisenberg anisotropic quantum spin-1/2 chain threaded by a time-dependent magnetic flux. In the spirit of the recently developed generalized hydrodynamics (GHD), we exploit the integrability of the model for any flux values to derive an exact description of the dynamics in the limit of slowly varying flux: the state of the system is described at any time by a time-dependent generalized Gibbs ensemble. Two dynamical regimes emerge according to the value of the anisotropy Δ. For |Δ|>1, reversibility is preserved: the initial state is always recovered whenever the flux is brought back to zero. On the contrary, for |Δ|