Wide quantum critical region of valence fluctuations: Origin of robust quantum criticality in quasicrystal Yb₁₅Al₃₄Au₅₁ under pressure

The mechanism of the emergence of robust quantum criticality in the heavy- electron quasicrystal YR₁₅Al₃₄Au₅₁ is analyzed theoretically. By constructing a minimal model for the quasicrystal and its crystalline approximant, which contain concentric shell structures with Yb and Al-Au clusters, we show that a set of quantum critical points of the first-order valence transition of Yb appears as spots in the ground-state phase diagram. Their critical regions overlap each other, giving rise to a wide quantum critical region. This well explains the robust criticality observed in YR₁₅Al₃₄Au₅₁ under pressure, and predicts the emergence of the common criticality in the crystalline approximant under pressure. The wider critical region in the quasicrystal than that in the crystalline approximant in the T-P phase diagram and the field-induced valence-crossover 'region' in the T-H phase diagram are predicted to appear