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 \ensuremath{\Vert}scrJ\ensuremath{\Vert}${T}_{K}$ and \ensuremath{\Vert}scrJ\ensuremath{\Vert}\ensuremath{\gtrsim}${T}_{K}$ for both ferromagnetic and antiferromagnetic scrJ, considering in particular the antiferromagnetic regime scrJ/${T}_{K}$\ensuremath{\approxeq}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${\mathrm{S}}_{1}$\ensuremath{\cdot}${\mathrm{S}}_{2}$ 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/${T}_{K}$\ensuremath{\approxeq}2.4 regime, and give possible explanations for this difference with the renormalization-group results.