Continuous Quantum Phase Transition in a Kondo Lattice Model

We study the magnetic quantum phase transition in an anisotropic Kondo lattice model. The dynamical competition between the RKKY and Kondo interactions is treated using an extended dynamic mean field theory appropriate for both the antiferromagnetic and paramagnetic phases. A quantum Monte Carlo approach is used, which is able to reach very low temperatures, of the order of 1% of the bare Kondo scale. We find that the finite-temperature magnetic transition, which occurs for sufficiently large RKKY interactions, is first order. The extrapolated zero-temperature magnetic transition, on the other hand, is continuous and locally critical.

Figure 1

Temperature dependence of the staggered magnetization $m_{\mathrm{A}\mathrm{F}}$ (a) and the normalized static local susceptibility (b) for the values of the RKKY interaction $I/T_K^0=3.0$ (squared curves) and 1.5 (diamond curves).

Figure 2

(a) The Néel temperature (solid dots) and $E_{\mathrm{l}\mathrm{o}\mathrm{c}}^{*}$ (open diamonds) as a function of $I/T_K^0$, the ratio of the RKKY interaction to the bare Kondo scale; (b) the staggered magnetization (solid dots) as a function of $I/T_K^0$, at $T=0.011T_K^0$. $E_{\mathrm{l}\mathrm{o}\mathrm{c}}^{*}$ characterizes the coherence scale of the paramagnetic solution (see the main text). The solid and dashed lines are guides to the eye.

Figure 3

Curie constant $\mathcal{C}$ in the nominally “paramagnetic” solution as a function of $I/T_K^0$. Inset: the local susceptibility versus Matsubara frequency ${\omega }_n$ for $I=2T_K^0$ at various temperatures; the jump at ${\omega }_n=0$ measures $\mathcal{C}/T$.

Figure 4

The normalized local susceptibility versus Matsubara frequency, at $T=0.011T_K^0$. The legend specifies $I/T_K^0$.