  We investigate the soft mode at the QCD critical point (CP) on the basis of
the functional renormalization group. We calculate the spectral functions in
the meson channels in the two-flavor quark--meson model. Our result shows that
the energy of the peak position of the particle--hole mode in the sigma channel
becomes vanishingly small as the system approaches the QCD CP, which is a
manifestation of the softening of the phonon mode. We also extract the
dispersion curves of the mesonic and the phonon mode, a hydrodynamic mode which
leads to a finding that the dispersion curve of the sigma-mesonic mode crosses
the light-cone into the space-like momentum region, and then eventually merges
into the phonon mode as the system approaches further close to the CP. This may
suggest that the sigma-mesonic mode forms the soft mode together with the
hydrodynamic mode at the CP.
