  Recent discoveries of a new type of quantum criticality arising from
Yb-valence fluctuations in Yb-based metal in periodic crystal and quasicrystal
have opened a new class of quantum critical phenomena in correlated electron
systems. To clarify whether this new concept can be generalized to other
rare-earth-based semimetal and insulator, we study SmS which exhibits
golden-black phase transition under pressure. By constructing the model for
SmS, we show that Coulomb repulsion between 4f and 5d orbitals at Sm drives
first-order valence transition (FOVT) and semimetal-to-insulator transition
(MIT) simultaneously, which explains the golden-black phase transition. We
clarify the ground-state phase diagram for the FOVT and MIT by identifying the
quantum critical point of the FOVT. We find that exciton condensates in both
semimetal and insulator phases. Our result explains measured peak anomalies in
the specific heat and compressibility in pressurized golden SmS and provides a
cue to clarify recently-observed anomalies in black SmS.
