  First principles density functional theory (DFT) simulations of
antiferroelectric (AFE) PbZrO$_3$ and PbHfO$_3$ reveal a dynamical instability
in the phonon spectra of their purported low temperature $Pbam$ ground states.
This instability doubles the $c$-axis of $Pbam$ and condenses five new small
amplitude phonon modes giving rise to an 80-atom $Pnam$ structure. Compared
with $Pbam$, the stability of this structure is slightly enhanced and highly
reproducible as demonstrated through using different DFT codes and different
treatments of electronic exchange & correlation interactions. This suggests
that $Pnam$ is a new candidate for the low temperature ground state of both
materials. With this finding, we bring parity between the AFE archetypes and
recent observations of a very similar AFE phase in doped or electrostatically
engineered BiFeO$_3$.
