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arXiv:2404.11955

Electrical control of a Kondo spin screening cloud

Ngoc Han Tu, Dong-Hoon Kim, Kim, Minsoo L., Jeongmin Shim, Ryo Ito, David Pomaranski, Ivan Valerievich Borzenets, Arne Ludwig, Andreas Dirk Wieck, H.-S. Sim, Michihisa Yamamoto

Published Apr 18, 2024• 1 citation
arXivHTMLPDF

Abstract

Quantitative analysis of quantum many-body systems, consisting of numerous itinerant electrons that interact with localized spins or electrons, is a long-standing issue. The Kondo cloud, a quantum many-body object of conduction electrons that screens a single localized spin, is the building block of such strongly correlated electronic systems. While quantitative analysis of the Kondo cloud associated with a single magnetic impurity is well established for uniform conduction electrons, the fundamental properties of a deformed Kondo cloud influenced by conduction electrons with a modulated density of states remain unsolved. Here we report engineering of the Kondo cloud deformation by confining a part of the cloud into a quantum box called the Kondo box that mimics realistic material systems. We demonstrate quantitative control of the Kondo cloud by developing a way of tuning quantum interference in the box and monitoring the Kondo entanglement. The temperature dependence of the entanglement reveals counterintuitively that the cloud shape is altered mainly outside the box although the quantum interference in the box is tuned. Our work provides a way to simulate various strongly correlated systems by integrating the Kondo cloud, which is not possible in the current theoretical framework.

DOI
10.48550/arxiv.2404.11955

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Quantitative analysis of quantum many-body systems, consisting of numerous itinerant electrons that interact with localized spins or electrons, is a long-standing issue. The Kondo cloud, a quantum many-body object of conduction electrons that screens a single localized spin, is the building block of such strongly correlated electronic systems. While quantitative analysis of the Kondo cloud associated with a single magnetic impurity is well established for uniform conduction electrons, the fundamental properties of a deformed Kondo cloud influenced by conduction electrons with a modulated density of states remain unsolved. Here we report engineering of the Kondo cloud deformation by confining a part of the cloud into a quantum box called the Kondo box that mimics realistic material systems. We demonstrate quantitative control of the Kondo cloud by developing a way of tuning quantum interference in the box and monitoring the Kondo entanglement. The temperature dependence of the entanglement reveals counterintuitively that the cloud shape is altered mainly outside the box although the quantum interference in the box is tuned. Our work provides a way to simulate various strongly correlated systems by integrating the Kondo cloud, which is not possible in the current theoretical framework.
Quantum entanglement permeates the complex ground states of correlated electron materials defying single-particle descriptions. Coupled magnetic atoms have potential as model systems for entanglement in condensed matter giving the opportunity to create artificial many-body states which can be controlled by tuning the underlying interactions. They provide an avenue to unravel the complexities of correlated-electron materials. Here we use low temperature scanning tunnelling microscopy (STM) and atomic manipulation to tune entanglement in chains of magnetic atoms. We find that a Kondo singlet state can emerge from this entanglement. The many electron Kondo state is based on the screening of the entangled spin ground state of the chain by substrate electrons and can be engineered to envelop at least ten magnetic atoms. The concomitant Kondo resonance measured in the differential conductance enables the electric read-out of entanglement. By tuning composition and coupling strength within atomic chains it is possible to create model spin chains with defined entanglement. This lays the foundation for a new class of experiments to construct exotic correlated-electron materials atom by atom.
We analyze the single-channel Kondo model using the recently developed unitary renormalization group (URG) method, and obtain a comprehensive understanding of the Kondo screening cloud. The fixed-point low-energy Hamiltonian enables the computation of a plethora of thermodynamic quantities (specific heat, susceptibility, Wilson ratio, etc.) as well as spectral functions, all of which are found to be in excellent agreement with known results. By integrating out the impurity, we obtain an effective Hamiltonian for the excitations of the electrons comprising the Kondo cloud. This is found to contain both k-space number-diagonal (Fermi liquid) as well off-diagonal four-fermion scattering terms. Our conclusions are reinforced by a URG study of the two-particle entanglement and many-body correlations among members of the Kondo cloud and impurity. The entanglement between the impurity and a cloud electron, as well as between any two cloud electrons, is found to increase under flow towards the singlet ground state at the strong-coupling fixed point. Both the number-diagonal and off-diagonal correlations within the conduction cloud are also found to increase as the impurity is screened under the flow, and the latter are found to be responsible for the macroscopic entanglement of the Kondo-singlet ground state. The unitary RG flow enables an analytic computation of the phase shifts suffered by the conduction electrons at the strong-coupling fixed point. This reveals an orthogonality catastrophe between the local moment and strong-coupling ground states, and is related to a change in the Luttinger volume of the conduction bath. Our results offer fresh insight on the nature of the emergent many-particle entanglement within the Kondo cloud, and pave the way for further investigations in more exotic contexts such as the fixed point of the over-screened multi-channel Kondo problem.
We analyze the single-channel Kondo model using the recently developed unitary renormalization-group (URG) method and obtain a comprehensive understanding of the Kondo screening cloud. The fixed-point low-energy Hamiltonian enables the computation of a plethora of thermodynamic quantities (specific heat, susceptibility, Wilson ratio, etc.) as well as spectral functions, all of which are found to be in good agreement with known results. By integrating out the impurity, we obtain an effective Hamiltonian for the excitations of the electrons comprising the Kondo cloud. This is found to contain both kkk-space number diagonal (Fermi liquid) and off-diagonal four-fermion scattering terms. Our conclusions are reinforced by a URG study of the two-particle entanglement and many-body correlations among members of the Kondo cloud and impurity. The entanglement between the impurity and a cloud electron, as well as between any two cloud electrons, is found to increase under flow towards the singlet ground state at the strong-coupling fixed point. Both the number diagonal and off-diagonal correlations within the conduction cloud are also found to increase as the impurity is screened under the flow, and the latter are found to be responsible for the macroscopic entanglement of the Kondo-singlet ground state. The URG flow enables an analytic computation of the phase shifts suffered by the conduction electrons at the strong-coupling fixed point. This reveals an orthogonality catastrophe between the local-moment and strong-coupling ground states and is related to a change in the Luttinger volume of the conduction bath under the crossover to strong coupling. Our results offer fresh insight into the nature of the emergent many-particle entanglement within the Kondo cloud and pave the way for further investigations in more exotic contexts such as the fixed point of the overscreened multichannel Kondo problem.
A quantum coherent screening cloud around a magnetic impurity in metallic systems is the hallmark of the antiferromagnetic Kondo effect. Despite the central role of the Kondo effect in quantum materials, the structure of quantum correlations of the screening cloud has defied direct observations. In this work, we introduce a machine-learning algorithm that allows one to spatially map the entangled electronic modes in the vicinity of the impurity site from experimentally accessible data. We demonstrate that local correlators allow reconstruction of the local many-body correlation entropy in real space in a double Kondo system with overlapping entanglement clouds. Our machine-learning methodology allows bypassing the typical requirement of measuring long-range nonlocal correlators with conventional methods. We show that our machine-learning algorithm is transferable between different Kondo system sizes, and we show its robustness in the presence of noisy correlators. Our work establishes the potential machine-learning methods to map many-body entanglement from real-space measurements.
When a local impurity spin interacts with conduction electrons whose density of states (DOS) has a (pseudo)gap or diverges at the Fermi energy, a local moment (LM) phase can be favored over a Kondo phase. Theoretically studying quantum entanglement between the impurity and conduction electrons, we demonstrate that conduction electrons form an LM spin cloud in general LM phases, which corresponds to, but has a fundamental difference from, the Kondo cloud screening the impurity spin in the Kondo phase. The LM cloud algebraically decays over the distance from the impurity when the DOS has a pseudogap or divergence, and exponentially when it has a hard gap. We find an LM cloud length, a single length scale characterizing a universal form of the LM cloud. The findings are supported by both analytic theories and numerical computations.
Abstract The screening of an impurity spin in the Kondo model occurs over a characteristic length scale ξ K , that defines the size of the Kondo screening cloud or ‘mist’. The presence of such a length scale in experimental and numerical results is rather subtle. A consistent way to show the presence of the screening cloud is to demonstrate scaling in the spatial correlations in terms of the single variable, r / ξ K instead of the correlations depending on r and ξ K separately. Here we study the paradigmatic one channel Kondo model using a spin chain representation, with an impurity spin at one end of the chain coupled with a strength J K ′ . Using Fermi liquid theory combined with numerical results, we obtain new high precision estimates of the non-universal terms in the entanglement entropy which leads to a verification of the expected non-integer ground-state degeneracy, g. This then allows us to study the impurity contribution to the entanglement in detail. If the impurity coupling J K ′ is varied, a precise determination of ξ K can then be obtained. The length scale, ξ K , is then shown to characterize the scaling of both the uniform and alternating part of a measure of the magnetization of part of an odd length chain.