Critical Kondo Destruction in a Pseudogap Anderson Model: Scaling and Relaxational Dynamics

We study the pseudogap Anderson model as a prototype system for critical Kondo destruction. We obtain finite-temperature ($T$) scaling functions near its quantum-critical point, by using a continuous-time quantum Monte Carlo method and also considering a dynamical large-$N$ limit. We are able to determine the behavior of the scaling functions in the typically difficult to access quantum-relaxational regime ($\hslash \omega <k_{B}T$) and conclude that the relaxation rates for both the spin and single-particle excitations are linear in temperature. We discuss the implications of these results for the quantum-critical phenomena in heavy-fermion metals.

Figure 1

Scaling functions for the imaginary part of (a) Green’s function $\mathcal{G}(\omega ,T)$ and (b) susceptibility $\chi (\omega ,T)$ for $r=0.3$ and $\kappa =0.5$ at the critical $J_c\approx 1.54$ (with $T_K^0\approx 0.3D$ for $r=0$). Both functions display $\omega /T$ scaling with scaling functions $\Phi$ obeying $\Phi (\omega /T\to 0)\to c$ or 0 for $\mathcal{G}$ or $\chi$, where $c\ne 0$ is a constant. (c), (d) The scaling functions in imaginary time.

Figure 2

Dynamical local susceptibility $\chi (\tau ,T)$ versus $\tau T$ for $r=0.4$ and ${\Gamma }_0=0.1D$ with $U=0$ and $U=0.3D$ (a). Finite-temperature scaling of the Binder cumulant $B(U,T)$ as a function of $U$ at various temperatures (b); error bars are obtained from a jackknife error analysis. From the intersection of the curves we determine the critical point to be $U_c(r=0.4)/D=0.085\pm 0.002$.

Figure 3

Scaling of (a) Green’s function $\mathcal{G}(\tau ,T)$ and (b) susceptibility $\chi (\tau ,T)$ at the QCP for $r=0.4$, ${\Gamma }_0=0.1D$, and $U_c(r=0.4)=0.085D$. The Kondo temperature in this case is $T_K^0\approx 0.029D$ (for $r=0$). For $T/D<5\times {10}^{-3}$, we observe collapse of the data over several decades for more than two decades of the parameter $(\pi T)/\sin (\pi \tau T)$, i.e., ${\mathcal{G}}_c(\tau ,T)=\Psi [\pi T/\sin (\pi \tau T)]$ and ${\chi }_c(\tau ,T)=\Phi [\pi T/\sin (\pi \tau T)]$. $\Psi (y\to 0)\propto y^{\delta }$ with $\delta =0.57(5)$, and $\Phi (y\to 0)\propto y^{1-x}$ with $x=0.68(3)$.