  We present the first calculation of fermion spectral function at finite
temperature in quark-meson model in the framework of the functional
renormalization group (FRG). We compare the results in two truncations, after
first evolving flow equation of effective potential, we investigate the
spectral function either by taking the IR values as input to calculate one-loop
self-energy or by taking the scale-dependent values as input to evolve the flow
equation of the fermion two-point function. The latter one is a self-consistent
procedure in the framework of FRG. In both truncations, we find a multi-peak
structure in the spectral function, indicating quark collective excitations
realized in terms of the Landau damping. However, in contrast to fermion
zero-mode in the one-loop truncation, we find a fermion soft-mode in the
self-consistent truncation, which approaches the zero-mode as temperature
increases.
