  Pyrochlore systems ($A_{2}B_{2}O_{7}$) with $A$-site rare-earth local moments
and $B$-site $5d$ conduction electrons offer excellent material platforms for
the discovery of exotic quantum many-body ground states. Notable examples
include U(1) quantum spin liquid of the local moments and semimetallic
non-Fermi liquid of the conduction electrons. Here we investigate emergent
quantum phases and their transitions driven by the Kondo lattice coupling
between such highly entangled quantum ground states. Using the renormalization
group method, it is shown that weak Kondo lattice coupling is irrelevant,
leading to a fractionalized semimetal phase with decoupled local moments and
conduction electrons. Upon increasing the Kondo lattice coupling, this phase is
unstable to the formation of broken symmetry states. Particularly important is
the opposing influence of the Kondo lattice coupling and long-range Coulomb
interaction. The former prefers to break the particle-hole symmetry while the
latter tends to restore it. The characteristic competition leads to possibly
multiple phase transitions, first from a fractionalized semimetal phase to a
fractionalized Fermi surface state with particle-hole pockets, followed by the
second transition to a fractionalized ferromagnetic state. Multiscale quantum
critical behaviors appear at nonzero temperatures and with external magnetic
field near such quantum phase transitions. We discuss the implication of these
results to the experiments on Pr$_2$Ir$_2$O$_7$.
