  We study the antiferromagnetic phase of the Kondo lattice model on bipartite
lattices at half-filling using the dynamical mean-field theory with numerical
renormalization group as the impurity solver, focusing on the detailed
structure of the spectral function, self-energy, and optical conductivity. We
discuss the deviations from the simple hybridization picture, which adequately
describes the overall band structure of the system (four quasiparticle branches
in the reduced Brillouin zone), but neglects all effects of the
inelastic-scattering processes. These lead to additional structure inside the
bands, in particular asymmetric resonances or dips that become more pronounced
in the strong-coupling regime close to the antiferromagnet-paramagnetic Kondo
insulator quantum phase transition. These features, which we name "spin
resonances", appear generically in all models where the $f$-orbital electrons
are itinerant (large Fermi surface) and there is N\'eel antiferromagnetic order
(staggered magnetization), such as periodic Anderson model and Kondo lattice
model with antiferromagneitc Kondo coupling, but are absent in
antiferromagnetic phases with localized $f$-orbital electrons (small Fermi
surface), such as the Kondo lattice model with ferromagnetic Kondo coupling. We
show that with increasing temperature and external magnetic-field the spin
resonances become suppressed at the same time as the staggered magnetization is
reduced. Optical conductivity $\sigma(\Omega)$ has a threshold associated with
the indirect gap, followed by a plateau of low conductivity and the main peak
associated with the direct gap, while the spin resonances are reflected as a
secondary peak or a hump close to the main optical peak. This work demonstrates
the utility of high-spectral-resolution impurity solvers to study the dynamical
properties of strongly correlated fermion systems.
