Monte Carlo simulation of lattice systems with RKKY interaction

Nefedev, Konstantin; Belokon, V. I.; Kapitan, Vitalii; Dyachenko, O.

doi:10.1088/1742-6596/490/1/012163

Cited by 8 publications

(3 citation statements)

References 15 publications

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“…While the oscillations are very pronounced for an isotropic dispersion of the conduction electrons in 1d, resulting in significant corrections in 1d, the derivative becomes R independent in 3d -see Eq. (61) in Ref. [32].…”

Section: Low-energy Effective Multi-impurity Modelmentioning

confidence: 99%

“…The interest for the two-impurity problem originates in the Doniach scenario [9] for Heavy Fermions (HF) [1] which relates the origin of the magnetic ordering found in some of the HFs to the competition between the singleion Kondo effect [8] screening the local moments and the RKKY interaction [52][53][54][55][56][57][58][59][60][61] favoring magnetic ordering of those moments. Although lacking a rigorous mathematical prove, such appealing visualizations of the complex physics in HF [4,16,62] are popular even today [62], since it provides a simple picture that can intuitively be grasped.…”

Section: B Preliminariesmentioning

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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Section: Low-energy Effective Multi-impurity Modelmentioning

confidence: 99%

Section: B Preliminariesmentioning

confidence: 99%

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

Eickhoff,

Anders

2020

Preprint

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“…The RKKY interaction has been investigated for more than 60 years and it is well established, that the anisotropy caused by the lattice of the host has a strong influence on the RKKY iteraction [71][72][73][74][75][76]. However, for a large Kondo-coupling J K and small U/Γ 0 respectively, the Kondo effect has a strong influence on the spin-spin correlation function and the textbook expression for the RKKY interaction is not sufficient to describe the magnetic order [70].…”

Section: Simple Cubic Latticementioning

confidence: 99%

Effective low-energy description of the two-impurity Anderson model: RKKY interaction and quantum criticality

2018

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We show that the RKKY interaction in the two-impurity Anderson model comprise two contributions: a ferromagnetic part stemming from the symmetrized hybridization functions and an anti-ferromagnetic part. We demonstrate that this anti-ferromagnetic contribution can also be generated by an effective local tunneling term between the two impurities. This tunneling can be analytically calculated for particle-hole symmetric impurities. Replacing the full hybridization functions by the symmetric part and this tunneling term leads to the identical low-temperature fixed point spectrum in the numerical renormalization group. Compensating this tunneling term is used to restore the Varma-Jones quantum critical point between a strong coupling phase and a local singlet phase even in the absence of particle-hole symmetry in the hybridization functions. We analytically investigate the spatial frequencies of the effective tunneling term based on the combination of the band dispersion and the shape of the Fermi surface. Numerical renormalization group calculations provide a comparison of the distance dependent tunneling term and the local spin-spin correlation function. Derivations between the spatial dependency of the full spin-spin correlation function and the textbook RKKY interaction are reported.

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High Performance Calculation of Magnetic Properties and Simulation of Nonequilibrium Phenomena in Nanofilms

Kapitan

Nefedev

2014

Modeling, Simulation and Optimization of Complex Processes - HPSC 2012

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Images of surface topography of ultrathin magnetic films have been used for Monte Carlo simulations in the framework of the ferromagnetic Ising model to study the hysteresis and thermal properties of nanomaterials. For high performance calculations was used super-scalable parallel algorithm for the finding of the equilibrium configuration. The changing of a distribution of spins on the surface during the reversal of the magnetization and the dynamics of nanodomain structure of thin magnetic films under the influence of changing external magnetic field was investigated.

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Monte Carlo simulation of lattice systems with RKKY interaction

Cited by 8 publications

References 15 publications

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

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

Effective low-energy description of the two-impurity Anderson model: RKKY interaction and quantum criticality

High Performance Calculation of Magnetic Properties and Simulation of Nonequilibrium Phenomena in Nanofilms

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