  We study the phase diagram of two-flavor massless QCD at finite baryon
density by applying the functional renormalization group (FRG) for a
quark-meson model with $\sigma, \pi$, and $\omega$ mesons. The dynamical
fluctuations of quarks, $\sigma$, and $\pi$ are included into the flow
equations, while the amplitudes of $\omega$-fields are also allowed to
fluctuate. At high temperature the effects of the $\omega$-field on the phase
boundary are qualitatively similar to the mean-field calculations; the phase
boundary is shifted to the higher chemical potential region. As the temperature
is lowered, however, the transition line bends back to the lower chemical
potential region, irrespective to the strength of the vector coupling. In our
FRG calculations, the driving force of the low temperature first order line is
the fluctuations rather the quark density, and the effects of $\omega$-fields
have little impact. At low temperature, the effective potential at small
$\sigma$ field is very sensitive to the infrared cutoff scale, and this
significantly affects our determination of the phase boundaries. The critical
chemical potential at the tricritical point is affected by the $\omega$-field
effects but its critical temperature stays around the similar value. Some
caveats are given in interpreting our model results.
