Equilibrium and real-time properties of the spin correlation function in the two-impurity Kondo model

Abstract

We investigate the equilibrium and real-time properties of the spin correlation function S1 S2 in the two-impurity Kondo model for different distances R between the two-impurity spins. It is shown that the competition between the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction and the Kondo effect governs the amplitude of S1 S2 . For distances R exceeding the Kondo length scale, the Kondo effect also has a profound effect on the sign of the correlation function. For ferromagnetic Heisenberg couplings J between the impurities and the conduction band, the Kondo effect is absent and the correlation function only decays for distances beyond a certain length scale introduced by finite temperature. The real-time dynamics after a sudden quench of the system reveals that correlations propagate through the conduction band with Fermi velocity. We identify two distinct timescales for the long time behavior which reflects that for small J the system is driven by the RKKY interaction while for large J the Kondo effect dominates. Interestingly, we find that at certain distances a one-dimensional dispersion obeying (k) = (−k) may lead to a local parity conservation of the impurities such that S1 S2 becomes a conserved quantity for long times and does not decay to its equilibrium value.

Kondo holes in strongly correlated impurity arrays: RKKY driven Kondo screening and hole-hole interactions

“…5 of Ref. [74]. However, a finite temperature T introduces a natural cut off energy scale such that the ratio of K ex hh /T determines the strength of the spin correlation.…”

Strongly correlated multi-impurity models: The crossover from a single-impurity problem to lattice models

“…This mapping was previously investigated [32] in the two-impurity Anderson model (N f = 2) where the two conduction bands represent states with even and with odd parity. In this case, one can either use the full energy dependency of the even-parity and the odd-parity band [11,12,76,77] in an numerical renormalization group (NRG) [39] calculation, or investigate the mapped Hamiltonian (11) with a particle-hole symmetric band density of states. Both Hamiltonians, the original MIAM, as well as the mapped Hamiltonian, produced the same RG fixed points for a featureless initial ρ(ω), and the same spin-spin correlation functions in the wide band limit, establishing the quality of the mapping for N f = 2.…”