  We use an unbiased, continuous-time quantum Monte Carlo method to address the
possibility of a zero-temperature phase without charge-density-wave (CDW) order
in the Holstein and, by extension, the Holstein-Hubbard model on the
half-filled square lattice. In particular, we present results spanning the
whole range of phonon frequencies, allowing us to use the well understood
adiabatic and antiadiabatic limits as reference points. For all parameters
considered, our data suggest that CDW correlations are stronger than pairing
correlations even at very low temperatures. These findings are compatible with
a CDW ground state that is also suggested by theoretical arguments.
