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Register a new userTwo-Impurity Anderson model in an Antiferromagnetic metal: zero-bandwidth limit
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R. Allub
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We study the zero-bandwidth limit of the two-impurity Anderson model in an antiferromagnetic (AF) metal. We calculate, for different values of the model parameters, the lowest excitation energy, the magnetic correlation $<mathbf{S}_{1}mathbf{S}_{2}>$ between the impurities, and the magnetic moment at each impurity site, as a function of the distance between the impurities and the temperature. At zero temperature, in the region of parameters corresponding to the Kondo regime of the impurities, we observe an interesting competition between the AF gap and the Kondo physics of the two impurities. When the impurities are close enough, the AF splitting governs the physics of the system and the local moments of the impurities are frozen, in a state with very strong ferromagnetic correlation between the impurities and roughly independent of the distance. On the contrary, when the impurities are sufficiently far apart and the AF gap is not too large, the scenario of the Kondo physics take place: non-magnetic ground state and the possibility of spin-flip excitation emerges and the ferromagnetic $<mathbf{S}_{1}mathbf{S}_{2}>$ decreases as the distance increases, but the complete decoupling of the impurities never occurs. In adition, the presence of the AF gap gives a non-zero magnetic moment at each impurity site, showing a non complete Kondo screening of the impurities in the system. We observe that the residual magnetic moment decreases when the distance between the impurities is increased.
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We investigate static and dynamical ground-state properties of the two-impurity Anderson model at half filling in the limit of vanishing impurity separation using the dynamical density-matrix renormalization group method. In the weak-coupling regime, we find a quantum phase transition as function of inter-impurity hopping driven by the charge degrees of freedom. For large values of the local Coulomb repulsion, the transition is driven instead by a competition between local and non-local magnetic correlations. We find evidence that, in contrast to the usual phenomenological picture, it seems to be the bare effective exchange interactions which trigger the observed transition.
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