Quantum Monte Carlo study of the two-impurity Kondo Hamiltonian

We investigate the magnetic properties of the Kondo two-impurity Hamiltonian with a recently introduced, essentially exact quantum Monte Carlo technique. We explore in particular the competition between Kondo effect, with Kondo temperature $T_K$, and Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions, with coupling constant scrJ. We simulate the regimes ‖scrJ‖$T_K$ and ‖scrJ‖≳$T_K$ for both ferromagnetic and antiferromagnetic scrJ, considering in particular the antiferromagnetic regime scrJ/$T_K$≊2.4 where anomalous behavior is predicted from renormalization-group calculations. Over the entire parameter range, we find that nearby impurity spin-spin correlations initially develop according to a RKKY effective Hamiltonian $H_{\mathrm{eff}}$=scrJ${\mathrm{S}}_1$⋅${\mathrm{S}}_2$ as the temperature is lowered; the correlations then saturate at around the Kondo temperature $T_K$. This result suggests an analogous picture for the lattice case, with long-range order developing if a ‘‘RKKY lattice’’ transition temperature is reached before Kondo quenching effects set in. We also find no evidence for anomalous staggered susceptibility behavior in the scrJ/$T_K$≊2.4 regime, and give possible explanations for this difference with the renormalization-group results.