How generalized hydrodynamics time evolution arises from a form factor expansion

The generalized hydrodynamics (GHD) formalism has become an invaluable tool for the study of spatially inhomogeneous quantum quenches in (1+1)-dimensional integrable models. The main paradigm of the GHD is that at late times local observables can be computed as generalized Gibbs ensemble averages with space-time dependent chemical potentials. It is, however, still unclear how this semiclassical GHD picture emerges out of the full quantum dynamics. We evaluate the quantum time evolution of local observables in spatially inhomogeneous quenches, based on the quench action method, where observables can be expressed in terms of a form factor expansion around a finite-entropy state. We show how the GHD formalism arises as the leading term in the form factor expansion, involving one particle-hole pair on top of the finite-entropy state. From this picture it is completely transparent how to compute quantum corrections to GHD, which arise from the higher terms in the form factor expansion. Our calculations are based on relativistic field theory results, though our arguments are likely generalizable to generic integrable models.