Dynamical Scaling of Charge and Spin Responses at a Kondo Destruction Quantum Critical Point

Quantum critical points often arise in metals perched at the border of an antiferromagnetic order. The recent observation of singular and dynamically scaling charge conductivity in an antiferromagnetic quantum critical heavy fermion metal implicates beyond-Landau quantum criticality. Here we study the charge and spin dynamics of a Kondo destruction quantum critical point (QCP), as realized in an SU(2)-symmetric Bose-Fermi Kondo model. We find that the critical exponents and scaling functions of the spin and single-particle responses of the QCP in the SU(2) case are essentially the same as those of the large-$N$ limit, showing that $1/N$ corrections are subleading. Building on this insight, we demonstrate that the charge responses at the Kondo destruction QCP are singular and obey $\omega /T$ scaling. This property persists at the Kondo destruction QCP of the SU(2)-symmetric Kondo lattice model.

Figure 1

Local spin susceptibility $\chi (\tau )$ at the QCP of (a) the dynamical large-$N$ limit (purple dashed line represents the analytically obtained leading $T=0$ behavior) and (b) the SU(2) case; and electron Green’s function $G(\tau )$ at the QCP of (c) the dynamical large-$N$ limit and (d) the SU(2) case. In (a), (c), the temperature $T$ is measured in $D$. In (b), (d), $\beta =1/T$.

Figure 2

Singular charge response of the $B$ field calculated in the dynamical large-$N$ limit (a) and extracted in the SU(2) case (b) obtained at the QCP. In (a), the temperature $T$ is in units of $D$. In (b), $\beta =1/T$.

Figure 3

$\omega /T$ scaling at the QCP. (a) The charge response, showing the spectral function of the $B$ field and (b) the spin response, showing the spectral function of $\mathbf{S}$, both in the dynamical large-$N$ limit. The temperature $T$ and $\omega$ are in units of $D$.

Figure 4

Singular charge response of the $B$ field calculated in the lattice model at the Kondo destruction QCP.