Relaxation dynamics of local observables in integrable systems

We show, using the quench action approach [Caux&Essler Phys. Rev. Lett. 110 (2013)], that the whole post-quench time evolution of an integrable system in the thermodynamic limit can be computed with a minimal set of data which are encoded in what we denote the generalized single-particle overlap coefficient sΨ00(λ). This function can be extracted from the thermodynamically leading part of the overlaps between the eigenstates of the model and the initial state. For a generic global quench the shape of sΨ00(λ) in the low momentum limit directly gives the exponent for the power law decay to the effective steady state. As an example we compute the time evolution of the static density-density correlation in the interacting Lieb-Liniger gas after a quench from a Bose-Einstein condensate. This shows an approach to equilibrium with power law t−3 which turns out to be independent of the post-quench interaction and of the considered observable.