Magnetic Quantum Phase Transition in an Anisotropic Kondo Lattice

The quantum phase transition between paramagnetic and antiferromagnetic phases of the Kondo lattice model with Ising anisotropy in the intersite exchange is studied within extended dynamical mean-field theory. Nonperturbative numerical solutions at zero temperature point to a continuous transition for both two- and three-dimensional magnetism. In the former case, the transition is associated with critical local physics, characterized by a vanishing Kondo scale and by an anomalous exponent in the dynamics close in value to that measured in heavy-fermion ${\mathrm{CeCu}}_{5.9}{\mathrm{Au}}_{0.1}$.

Figure 1

Converged values of $y\equiv [I{\chi }_{\mathrm{loc}}(0){]}^{-1}$ vs $x\equiv [I\chi (\mathit{Q},0){]}^{-1}$. In 3D (squares), Eq. (3) forces $y=\frac{1}{2}(1+x)+\frac{1}{2}\sqrt{x(x+2)}$ (dashed line) to approach $\frac{1}{2}$ as $x$ vanishes. In 2D (circles), both quantities vanish together according to $y=2/\ln (1+2/x)$ (solid line), signaling critical Kondo physics.

Figure 2

Peak and local static susceptibilities (in units of $T_K^0$) of PM and AFM solutions, along with the order parameter $m_{\mathrm{AFM}}$, for (a) 3D and (b) 2D magnetic fluctuations. AFM solutions for $\delta \equiv I/T_K^0\le {\delta }_{c,A}$ (where $m_{\mathrm{AFM}}=0$ self-consistently) coincide with PM solutions (with $m_{\mathrm{AFM}}\equiv 0$). Lines are guides to the eye.

Figure 3

(a) Extrapolation to zero of PM ${\chi }^{-1}(\mathit{Q},0)$ (squares) and AFM ${\chi }^{-1}(\mathit{Q},0)/20$ (circles) for 3D and 2D magnetism. (b) Real part of ${\chi }_{\mathrm{loc}}(\omega )$ for five $\delta$ values approaching ${\delta }_c$ in the 2D AFM phase. The dashed line is a fit to the logarithmically singular form that develops for $\delta \to {\delta }_c$.