Magnetic Kondo regimes in a frustrated half-filled trimer

Wójcik, Krzysztof P.; Weymann, Ireneusz; Kroha, Johann

doi:10.1103/physrevb.102.045144

Cited by 7 publications

(3 citation statements)

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“…In the last decades the role of magnetic frustration for HF has been discussed in the context of strongly correlated multi-impurity models [4,[33][34][35][36][37][38]. Since it was realized that the two-impurity problem lacks the complexity and the reported QCP appears to be an artifact of the approximation [11,12] made in the originally approach, nowadays the focus lies on models with three local moments coupled to an arbitrary number of conduction bands [33][34][35][36][37][38]. These papers in particular focus on the emergence of a frustration induced NFL fixed point that might be related to QCPs found in bulk materials.…”

Section: Numerical Renormalization Group Results For Multi-impurity P...mentioning

confidence: 99%

“…However, interesting physics can arises in problems that contain magnetically frustrated systems requiring at least three impurities [33-35, 37, 38]. Our mapping provides an ideal tool to investigate which physical condition the original model must fulfill in order to reach the critical parameter regimes reported for the trimer Kondo models [33][34][35][36][37][38].…”

Section: Classification Of the Multi-impurity Problem By The Rank(γ)mentioning

confidence: 99%

“…The quest for a many-impurity problem that is solvable, and reveals interesting competing phases connected by a true QCP, triggered the investigation of the frustrated three impurity spin problems [33][34][35][36][37][38]. The connection to bulk materials, however, remains unclear, although it might be very helpful to illustrate the possibility of emerging complex phases.…”

Section: Introductionmentioning

confidence: 99%

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

Eickhoff,

Anders

2020

Preprint

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We present a mapping of various correlated multi-impurity Anderson models to a cluster model coupled to a number of effective conduction bands capturing its essential low-energy physics. The major ingredient is the complex single-particle self energy matrix of the uncorrelated problem that encodes the influence to the host conduction band onto the dynamics of a set of correlated orbitals in a given geometry. While the real part of the self-energy matrix generates an effective hopping between the cluster orbitals, the imaginary part, or hybridization matrix, determines the coupling to the effective conduction electron bands in the mapped model. The rank of the hybridization matrix determines the number of independent screening channels of the problem, and allows the replacement of the phenomenological exhaustion criterion by a rigorous mathematical statement. This rank provides a distinction between multi-impurity models of first kind and of second kind. For the latter, there are insufficient screening channels available, so that a singlet ground state must be driven by the inter-cluster spin correlations. This classification provides a fundamental answer to the question, why ferromagnetic exchange interactions between local moments are irrelevant for the spin compensated ground state in dilute multi-impurity models, whereas the formation of large spins competes with the Kondo-scale in dense impurity arrays, without evoking a spin density wave. The low-temperature physics of three examples taken from the literature are deduced from the analytic structure of the mapped model, demonstrating the potential power of this approach. Numerical renormalization group calculations are presented for up to five site cluster. We investigate the appearance of frustration induced non-Fermi liquid fixed points in the trimer, and demonstrate the existence of several critical points of Kosterlitz-Thouless type at which ferromagnetic correlations suppress the screening of an additional effective spin-1/2 degree of freedom.

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