Kondo Destruction and Valence Fluctuations in an Anderson Model

Unconventional quantum criticality in heavy-fermion systems has been extensively analyzed in terms of a critical destruction of the Kondo effect. Motivated by a recent demonstration of quantum criticality in a mixed-valent heavy-fermion system, $\beta \mathrm{\text{−}}{\mathrm{YbAlB}}_4$, we study a particle-hole-asymmetric Anderson impurity model with a pseudogapped density of states. We demonstrate Kondo destruction at a mixed-valent quantum critical point, where a collapsing Kondo energy scale is accompanied by a singular charge-fluctuation spectrum. Both spin and charge responses scale with energy over temperature ($\omega /T$) and magnetic field over temperature ($H/T$). Implications for unconventional quantum criticality in mixed-valence heavy fermions are discussed.

Figure 1

(a) Binder cumulant $B(U,\beta )$ vs $U$ for $r=0.6$, ${\Gamma }_0=0.1D$, and ${ϵ}_d=-0.05D$, and the labeled temperatures. Error bars were obtained from a jackknife analysis of the CT-QMC data. (b) Blow up of the same data around the intersection of curves, which determines $U_c/D=0.06313\pm 0.0008$.

Figure 2

Valence and local spin properties vs $u=U/U_c-1$ for $r=0.6$, ${\Gamma }_0=0.1D$, and ${\epsilon }_d=-0.05D$: (a) Occupancy $⟨n_d⟩$ at the labeled temperatures [29]. The QCP ($u=0$) occurs at mixed valence, i.e., $⟨n_d⟩\ne 1$. (b) Local magnetization $M_{\mathrm{loc}}$, showing quenching of the impurity spin for $u<0$ but the emergence of a free local moment for $u>0$.

Figure 3

Local static spin susceptibility ${\chi }_s(T,U)$ for $r=0.6$, ${\Gamma }_0=0.1D$, and ${\epsilon }_d=-0.05D$ (a) vs $u=U/U_c-1$ at the labeled temperatures [29] and (b) vs $T$ at the critical point $U=U_c$.

Figure 4

Local static charge susceptibility ${\chi }_c(T,U)$ for $r=0.6$, ${\Gamma }_0=0.1D$, and ${\epsilon }_d=-0.05D$ (a) vs $u=U/U_c-1$ at the labeled temperatures [29] and (b) vs $T$ at the critical point $U=U_c$, where the discrepancy between CT-QMC and NRG data is due mainly to the difference in $U_c$ values. Inset: ${\chi }_c(T,U_c)$ over a wider range of $T$, showing the slow crossover behavior.

Figure 5

Scaling of critical spin and charge responses for $r=0.6$, ${\Gamma }_0=0.1D$, ${\epsilon }_d=-0.05D$ and $U\simeq U_c$: (a), (b) Dynamical spin and charge susceptibilities vs $\pi T/\sin (\pi \tau T)$ for seven temperatures listed in the legends. With each step down in $T$ (step up in $\beta$), the data extend to lower values of $\pi T/\sin (\pi \tau T)$. Both susceptibilities show excellent scaling collapse over two decades of $\pi T/\sin (\pi \tau T)$. (c), (d) Static spin and charge susceptibilities vs $H/T$ in the labeled local magnetic fields $H$.