  We study the return probability and its imaginary ($\tau$) time continuation
after a quench from a domain wall initial state in the XXZ spin chain, focusing
mainly on the region with anisotropy $|\Delta|< 1$. We establish exact Fredholm
determinant formulas for those, by exploiting a connection to the six vertex
model with domain wall boundary conditions. In imaginary time, we find the
expected scaling for a partition function of a statistical mechanical model of
area proportional to $\tau^2$, which reflects the fact that the model exhibits
the limit shape phenomenon. In real time, we observe that in the region
$|\Delta|<1$ the decay for large times $t$ is nowhere continuous as a function
of anisotropy: it is either gaussian at root of unity or exponential otherwise.
As an aside, we also determine that the front moves as $x_{\rm
f}(t)=t\sqrt{1-\Delta^2}$, by analytic continuation of known arctic curves in
the six vertex model. Exactly at $|\Delta|=1$, we find the return probability
decays as $e^{-\zeta(3/2) \sqrt{t/\pi}}t^{1/2}O(1)$. It is argued that this
result provides an upper bound on spin transport. In particular, it suggests
that transport should be diffusive at the isotropic point for this quench.
