  Inspired by classical results in integrable boundary quantum field theory, we
propose a definition of integrable initial states for quantum quenches in
lattice models. They are defined as the states which are annihilated by all
local conserved charges that are odd under space reflection. We show that this
class includes the states which can be related to integrable boundary
conditions in an appropriate rotated channel, in loose analogy with the picture
in quantum field theory. Furthermore, we provide an efficient method to test
integrability of given initial states. We revisit the recent literature of
global quenches in several models and show that, in all of the cases where
closed-form analytical results could be obtained, the initial state is
integrable according to our definition. In the prototypical example of the XXZ
spin-s chains we show that integrable states include two-site product states
but also larger families of matrix product states with arbitrary bond
dimension. We argue that our results could be practically useful for the study
of quantum quenches in generic integrable models.
