  It is widely accepted that local subsystems in isolated integrable quantum
systems equilibrate to generalized Gibbs ensembles. Here, we demonstrate the
failure of canonical generalized thermalization for a particular class of
initial states in certain types of interacting integrable models. Particularly,
we show that in the easy-axis regime of the quantum XXZ chain, pure
non-equilibrium initial states with no magnetic fluctuations instead locally
relax to squeezed generalized Gibbs ensembles, referring to exotic equilibrium
states governed by non-local equilibrium Hamiltonians with sub-extensive charge
fluctuations that violate the self-affine scaling. The behaviour at the
isotropic point is exceptional and depends on the initial state. We find that
relaxation from the N\'{e}el state is governed by extensive fluctuations and a
super-diffusive dynamical exponent compatible with the Kardar-Parisi-Zhang
universality. On the other hand, there are other non-fluctuating initial states
that display diffusive scaling. Our predictions can be directly tested in
state-of-the-art cold atomic experimental settings.
