Journal of the Physical Society of Japan DRAFT Robustness of Quantum Criticality of Valence Fluctuations

The mechanism of emergence of robust quantum criticality in Yb- and Ce-based heavy elec-tron 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 criti-cal 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 β-YbAlB4 showing unconventional quantum criticality