  We study paramagnetic quantum criticality in the periodic Anderson model
(PAM) using cellular dynamical mean-field theory, with the numerical
renormalization group (NRG) as an impurity solver. The PAM describes an
itinerant $c$ band hybridizing with a localized $f$ band. At $T=0$, it exhibits
a hybridization tuned Kondo breakdown quantum critical point (KB-QCP) from a
Kondo to an RKKY phase. At the KB-QCP, the $f$ band changes character from
itinerant to mainly localized, while the $c$ band remains itinerant. We
elucidate its nature in detail by performing a high-resolution, real-frequency
study of dynamical quantities. NRG allows us to study the quantum critical
non-Fermi-liquid (NFL) regime located between $T_{FL}<T_{NFL}$. Surprisingly,
self-consistency is essential to stabilize the NFL and the QCP. The
Fermi-liquid (FL) scale $T_{FL}$ decreases towards and vanishes at the QCP. At
$T=0$, we find the following properties. The $f$ quasiparticle (QP) weight
$Z_f$ decreases continuously as the QCP is approached from either side,
vanishing only at the QCP. Therefore, $Z_f$ is nonzero in both the Kondo and
the RKKY phase; hence, the FL QP comprise $c$ and $f$ electrons in both phases.
The Fermi surface (FS) volumes in the two phases differ. Whereas the large-FS
Kondo phase has a usual two-band structure, the small-FS RKKY phase has an
unexpected three-band structure. We provide a detailed analysis of
quasiparticle properties of both the Kondo and the RKKY phase. The FS
reconstruction is accompanied by the appearance of a Luttinger surface (LS) on
which the $f$ self-energy diverges. The FS and LS volumes are related to the
density by a generalized Luttinger sum rule. We interpret the small FS volume
and the emergent LS as evidence for $f$-electron fractionalization in the RKKY
phase. Our Hall coefficient and specific heat are in good qualitative agreement
with experiment.
