Therefore, the generalisation of the validity of \eqref{ss} to a larger class of initial states is not necessary here (however we mention it %as a conjecture
COMMENT: I thought there was something wrong here. My argument was: for circular drivings (see Sec. V) [...] However, I've just made the calculation for $B_0 = B_1$ and found a %CONSTANT curvature $K(t)= \omega/2$ !! Could you please check this?
I'm not sure about the implications beyond [...]. I think this is why Lyanda-Geller found [...]. This also means that the critical field possess an anomalous, non-trivial topology since the winding number is $n_K=1/2$! Should we briefly comment on this in Sec. V?
%\textcolor{red}{(``spontaneous'' may be more general b/c this effect is not limited to the ground state although it is mostly clearly seen for the ground state...)}
approximation, which we wouldn't need to do. Is there a reason? (in practice I know that in the well-converged cases, since everything is almost translationally invariant, there would be no difference, anyway, but it seems difficult to justify, since we have to use the same data)
\textbf{KC: %OK, we don't need to write about this average -- in practice it was identical in the middle of the chain at the level of $10^{-6}$, so I took the %averages for convenience, but it doesn't matter.} }