  We investigate numerically the inverse participation ratios in a spin-1/2 XXZ
chain, computed in the "Ising" basis (i.e., eigenstates of $\sigma^z_i$). We
consider in particular a quantity $T$, defined by summing the inverse
participation ratios of all the eigenstates in the zero magnetization sector of
a finite chain of length $N$, with open boundary conditions. From a dynamical
point of view, $T$ is proportional to the stationary return probability to an
initial basis state, averaged over all the basis states (initial conditions).
We find that $T$ exhibits an exponential growth, $T\sim\exp(aN)$, in the gapped
phase of the model and a linear scaling, $T\sim N$, in the gapless phase. These
two different behaviors are analyzed in terms of the distribution of the
participation ratios of individual eigenstates. We also investigate the effect
of next-nearest-neighbor interactions, which break the integrability of the
model. Although the massive phase of the non-integrable model also has
$T\sim\exp(aN)$, in the gapless phase $T$ appears to saturate to a constant
value.
