Whereas the standard expansion of the 'quantum field theory' belonging to the s-d exchange Kondo Hamiltonian for a spin impurity in a paramagnetic host metal describes the high-energy scattering, the alternative renormalised perturbation expansion describes the low-energy scattering. In the high-energy regime the scattering centre acts as if it was an anti-ferromagnetically coupled spin, but in the low-energy regime it acts as if it was a spin of a different magnitude that is ferromagnetically coupled. Correspondingly, it is shown that two different Hamiltonians can give rise to the same field theory. In solid state physics this equivalence is the generalisation of the Schrieffer-Wolff transformation (1960) between the Anderson (or Wolff) model and the spin- 1 / 2 Kondo Hamiltonian.
Whereas the standard expansion of the 'quantum field theory' belonging to the s-d exchange Kondo Hamiltonian for a spin impurity in a paramagnetic host metal describes the high-energy scattering, the alternative renormalised perturbation expansion describes the low-energy scattering. In the high-energy regime the scattering centre acts as if it was an anti-ferromagnetically coupled spin, but in the low-energy regime it acts as if it was a spin of a different magnitude that is ferromagnetically coupled. Correspondingly, it is shown that two different Hamiltonians can give rise to the same field theory. In solid state physics this equivalence is the generalisation of the Schrieffer-Wolff transformation (1960) between the Anderson (or Wolff) model and the spin- 1 / 2 Kondo Hamiltonian.
The Kondo effect, the screening of the spin of an impurity by the conduction electrons of a metallic host system, is a standard problem in solid state physics. At weak coupling strengths between the host system and a group of impurities, the Kondo competes with indirect (RKKY) exchange, mediated by the conduction electrons, which promotes magnetic order among the impurities.
This work deals with the physics emerging in impurity systems with spatially confined metallic host materials, relevant to the quantum dots and artificial nanostructures created by scanning tunnelling techniques. It is shown that (i) the finite system size leads to an unconventional reentrant competition, where the Kondo prevails at weak couplings in contradiction to the standard Doniach picture. (ii) A novel mechanism is proposed which ferromagnetically correlates the impurities' magnetic moments without any indirect exchange. (iii) In case of degenerate Fermi levels, a multi-channel Kondo effect is observed. (iv) In the regime of strong couplings magnetic ordering is shown to be driven by a novel inverse indirect magnetic exchange (IIME), which is mediated by magnetically inert Kondo singlets.
The evolution of this physics is studied from the single-impurity Kondo box limit via the Kondo-vs.-RKKY quantum box to the regime of the Kondo-lattice box. Key insights are gained analytically by deriving effective low-energy Hamiltonians in the respective regimes by perturbation theory, and numerically by means of density-matrix renormalisation group (DMRG), dynamical mean-field theory (DMFT), and full diagonalisation calculations.
The presented theoretical concept is robust against weak environmental influences. The predicted effects await an experimental confirmation and exploration.
Der Kondo-Effekt, die Abschirmung eines Storstellen-Spins durch Leitungselektronen eines metallischen Wirtssystems, ist ein Standardproblem in der Festkorperphysik. Bei schwachen Kopplungen zwischen dem Wirtssystem und einer Gruppe von Storstellen konkurriert er mit dem indirekten, durch die Leitungselektronen vermittelten (RKKY) Austausch, der magnetische Ordnungen der Storstellen begunstigt.
Die vorliegende Arbeit behandelt die Physik von Storstellensystemen mit raumlich eingeschrankten metallischen Wirtsmaterialien, die von groser Bedeutung ist fur Quantenpunkte und kunstliche Nanostrukturen, die mit Rastertunneltechniken erschaffen werden konnen. Es wird gezeigt, dass (i) die endliche Systemgrose zu einem unkonventionellen Wettstreit fuhrt, in dem der Kondo-Effekt sich entgegen den Standardvorstellungen nach Doniach bei kleinen Kopplungen durchsetzt. (ii) Ein neuartiger Mechanismus wird vorgeschlagen, der die magnetischen Momente von Storstellen ohne jeglichen indirekten Austausch ferromagnetisch korreliert. (iii) Im Fall von entarteten Fermikanten-Zustanden wird ein multi-channel finite-size Kondo-Effekt beobachtet. (iv) Magnetische Ordnung im Regime groser Kopplungen wird durch einen neuartigen inversen indirekten magnetischen Austausch (IIMA) verursacht, der durch magnetisch inerte Kondo-Singlets vermittelt wird.
Die Entwicklung dieser Physik wird untersucht von der Eine-Storstelle-Kondo-Box, uber die Kondo-vs.-RKKY-Quantum-Box, bis hin zum Regime der Kondo-Gitter-Box. Schlusselerkenntnisse werden analytisch gewonnen durch die storungstheoretische Ableitung von effektiven Niedrigenergie-Hamiltonoperatoren in den entsprechenden Grenzfallen und numerisch mithilfe von Dichtematrix-Renormierungsgruppe (DMRG), dynamischer Meanfield-Theorie (DMFT) und voller Diagonalisierung.
Das vorgestellte Konzept ist robust gegen schwache Umgebungseinflusse. Die vorhergesagten Effekte sehen einer experimentellen Bestatigung und Erforschung entgegen.
We revisit the Schrieffer-Wolff transformation and present a path integral version of this important canonical transformation. The equivalence between the low-energy sector of the Anderson model in the so-called Kondo regime and the spin-isotropic Kondo model is usually established via a canonical transformation performed on the Hamiltonian, followed by a projection. Here we present a path integral version of the Schrieffer-Wolff transformation which relates the functional integral form of the partition function of the Anderson model to that of its effective low-energy model. The resulting functional integral assumes the form of a spin path integral and includes a geometric phase factor, i.e. a Berry phase. Our approach stresses the underlying symmetries of the model and allows for a straightforward generalization of the transformation to more involved models. It thus not only sheds new light on a classical problem. It also offers a systematic route of obtaining effective low-energy models and higher order corrections. This is demonstrated by obtaining the full effective low-energy model of a quantum dot attached to two ferromagnetic leads.
It is well known that the free electron Kondo problem can be described by a one-dimensional (1D) model because only the s-wave part of the electronic wavefunction is affected by the Kondo coupling. Moreover, since only the spin degrees of freedom are involved in the Kondo interaction, and due to spin–charge separation in 1D, the universal low energy long distance physics of the Kondo model also arises when a magnetic impurity is coupled to the end of a gapless antiferromagnetic J 1 –J 2 spin- chain, where J 1 ( J 2 ) is the (next) nearest neighbor coupling. Experimental realizations of such spin chain models are possible and, using various analytical and numerical techniques, we present a detailed and quantitative comparison between the usual free electron Kondo model and such spin chain versions of the Kondo problem. For the gapless J 1 –J 2 spin chain two cases are studied, with zero next nearest neighbor coupling, J 2 = 0, and with a critical second-neighbor coupling, J 2 = J 2 c . We first focus on the spin chain impurity model with a critical second-neighbor antiferromagnetic exchange where a bulk marginal coupling present in the spin chain model for J 2 < J 2 c vanishes . There, the usual Kondo physics is recovered in the spin chain model in the low energy regime (up to negligible corrections, dropping as powers of inverse length or energy). At J 2 c the spin chain model is not exactly solvable and we demonstrate the equivalence to the Kondo problem by comparing density matrix renormalization group calculations on the frustrated spin chain model with exact Bethe ansatz calculations of the electronic Kondo problem. We then analyze the nearest neighbor model ( J 2 = 0) where a new kind of Kondo effect occurs due to the presence of the bulk marginal coupling. This marginal coupling slightly alters the β function for the Kondo coupling, leading to a slower variation of the Kondo temperature, T K , with the bare Kondo coupling. In their exact Bethe ansatz solution of this spin chain impurity model ( J 2 = 0), Frahm and Zvyagin noted this relation as well as the connection to the Kondo problem. Here, by numerically solving the Bethe ansatz equations we provide further evidence for the connection to Kondo physics and in addition we present low temperature quantum Monte Carlo results for the impurity susceptibility that further support this connection.
We show through a perturbative and an exact calculation using Wilson's renormalization methods that in the problem of two interacting Kondo impurities, on-site potential scattering generates a quantum-tunneling between the two impurities through a marginally relevant operator. The magnitude of this tunneling V12 depends on the spin-correlation between the two impurities. For exchange interactions between the moments comparable to the Kondo energy TK, V12 is typically much larger than TK. This implies that the heavy-fermion mass in this interesting range is determined by V12 rather than TK. The importance of these results for experiments in coupled Kondo dots is also pointed out.
The goal of this book is the investigation of physical effects at low energies caused by magnetic impurity adatoms, coupled to a small non-magnetic metallic substrate surface. Such systems can be understood with help of multi-impurity Kondo models, describing the substrate as a tight-binding model of finite-size and the impurities as quantum spins, which are antiferromagnetically coupled locally to their respective substrate sites. Focusing on one-dimensional finite-size systems with open boundary conditions at half-filling numerical exact diagonalisation and the variation of matrix product states (VMPS) method are used for the investigation. It is the aim to study finite-size effects in different regimes of the magnetic exchange interaction. For example due to the finite size of the system, the interplay of the Kondo effect and the indirect magnetic Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction between impurity spins is site dependent and non-trivial for at least three impurity Kondo systems. Furthermore evidence for an unconventional and novel magnetic coupling mechanism, causing magnetic order in the actually non-magnetic substrate, due to inverse indirect magnetic exchange, will be given.
We revisit the Schrieffer-Wolff transformation and present a path integral version of this important canonical transformation. The equivalence between the low-energy sector of the Anderson model in the so-called local moment regime and the spin-isotropic Kondo model is usually established via a canonical transformation performed on the Hamiltonian, followed by a projection. Here we present a path integral formulation of the Schrieffer-Wolff transformation which relates the functional integral form of the partition function of the Anderson model to that of its effective low-energy model. The resulting functional integral assumes the form of a spin path integral and includes a geometric phase factor, i.e. a Berry phase. Our approach stresses the underlying symmetries of the model and allows for a straightforward generalization of the transformation to more involved models. It thus not only sheds new light on a classic problem, it also offers a systematic route of obtaining effective low-energy models and higher order corrections. This is demonstrated by obtaining the effective low-energy model of a quantum dot attached to two ferromagnetic leads.