Robustness of Quantum Criticality of Valence Fluctuations

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.