  In a recent work by Gong and Ueda (arXiv:1710.05289), the classification of
(1+1)-dimensional quench dynamics for the ten Altland-Zirnbauer classes is
achieved, and entanglement-spectrum crossings of the time-dependent states for
the topological classes (AIII, DIII, CII, BDI, and D) are discovered as a
consequence of the bulk-edge correspondence. We note that, their classification
scheme relies on the limit that the energy spectrum of the post-quench
Hamiltonian is flat, because any finite band dispersion leads to the break down
of time-reversal and chiral symmetries for the parent Hamiltonian (which are
used for the classification). We show that, because of the reduction of
symmetry by finite energy dispersion, the gapless entanglement-spectrum
crossing in the flat-band limit in classes AIII, DIII, and CII is unstable, and
could be gapped without closing the bulk gap. The entanglement-spectrum
crossing in classes BDI and D is still stable against energy dispersion. We
show that the quench process for classes BDI and D can be understood as a
$\mathbb{Z}_2$ fermion parity pump, and the entanglement-spectrum crossing for
this case is protected by the conservation of fermion parity.
