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 TK, and Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions, with coupling constant scrJ. We simulate the regimes {}scrJ{}TK and {}scrJ{}{}TK for both ferromagnetic and antiferromagnetic scrJ, considering in particular the antiferromagnetic regime scrJ/TK{}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 Heff=scrJS₁{·}S₂ as the temperature is lowered; the correlations then saturate at around the Kondo temperature TK. 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/TK{}2.4 regime, and give possible explanations for this difference with the renormalization-group results.