  We first compare the geometric frameworks behind the Uhlmann and Berry phases
in a fiber-bundle language and then evaluate the Uhlmann phases of bosonic and
fermionic coherent states. The Uhlmann phases of both coherent states are shown
to carry geometric information and decrease smoothly with temperature.
Importantly, the Uhlmann phases approach the corresponding Berry phases as
temperature decreases. Together with previous examples in the literature, we
propose a correspondence between the Uhlmann and Berry phases in the
zero-temperature limit as a general property except some special cases and
present a conditional proof of the correspondence.
