  Using the XX- spin chain as an example we show that in general the asymptotic
expansion of the correlator at large distances is not given by the sum over the
low-lying particle-hole intermediate states. Only the first two terms in the
expansion agree with the predictions of the Luttinger liquid theory. The other
terms are in general given by the intermediate states with the particles and
holes with the quantum numbers far away from the Fermi- points (at the
distances of order of the length of the chain). We argue that the whole
expansion cannot be described by the Luttinger liquid theory.
