  Anfuso and Rosch [Phys. Rev. B 75, 144420 (2007)] showed that the
"topological" Haldane phase in a fermionic spin-1/2 ladder can be continuously
deformed into a "trivial" phase without explicitly breaking symmetries when
local charge fluctuations are taken into account. Within the framework of
symmetry protected topological phases, we revisit the model and demonstrate how
the Haldane phase can be adiabatically connected to a trivial phase due to
charge fluctuations. Furthermore, we show that the Haldane phase remains stable
as long as the system is symmetric under particular reflection symmetries.
