  The mechanism of emergence of robust quantum criticality in Yb- and Ce-based
heavy electron systems under pressure is analyzed theoretically. By
constructing a minimal model for quasicrystal Yb15Al34Au51 and its approximant,
we show that quantum critical points of the first-order valence transition of
Yb appear in the ground-state phase diagram with their critical regimes being
overlapped to be unified, giving rise to a wide quantum critical regime. This
well explains the robust unconventional criticality observed in Yb15Al34Au51
under pressure. We also discuss broader applicability of this mechanism to
other Yb- and Ce-based systems such as beta-YbAlB4 showing unconventional
quantum criticality.
