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arXiv:2012.13327 · SciPost Physics

Resolving the nonequilibrium Kondo singlet in energy- and position-space using quantum measurements

André Erpenbeck, Guy Cohen

Published Jun 11, 2021• 16 citations
arXivHTMLPDF

Abstract

The Kondo effect, a hallmark of strong correlation physics, is characterized by the formation of an extended cloud of singlet states around magnetic impurities at low temperatures. While many implications of the Kondo cloud's existence have been verified, the existence of the singlet cloud itself has not been directly demonstrated. We suggest a route for such a demonstration by considering an observable that has no classical analog, but is still experimentally measurable: ``singlet weights'', or projections onto particular entangled two-particle states. Using approximate theoretical arguments, we show that it is possible to construct highly specific energy- and position-resolved probes of Kondo correlations. Furthermore, we consider a quantum transport setup that can be driven away from equilibrium by a bias voltage. There, we show that singlet weights are enhanced by voltage even as the Kondo effect is weakened by it. This exposes a patently nonequilibrium mechanism for the generation of Kondo-like entanglement that is inherently different from its equilibrium counterpart.

DOI
10.21468/scipostphys.10.6.142

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The Kondo effect, a hallmark of strong correlation physics, is characterized by the formation of an extended cloud of singlet states around magnetic impurities at low temperatures. While many implications of the Kondo cloud's existence have been verified, the existence of the singlet cloud itself has not been directly demonstrated. We suggest a route for such a demonstration by considering an observable that has no classical analog, but is still experimentally measurable: ``singlet weights'', or projections onto particular entangled two-particle states. Using approximate theoretical arguments, we show that it is possible to construct highly specific energy- and position-resolved probes of Kondo correlations. Furthermore, we consider a quantum transport setup that can be driven away from equilibrium by a bias voltage. There, we show that singlet weights are enhanced by voltage even as the Kondo effect is weakened by it. This exposes a patently nonequilibrium mechanism for the generation of Kondo-like entanglement that is inherently different from its equilibrium counterpart.
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Connecting single-layer ttt-JJJ to Kondo lattice models: Exploration with cold atoms
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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.
The Kondo singlet---a many-body state formed by entanglement between a localized spin and the Fermi sea---has been studied extensively through its transport signatures in quantum dots. Here we report a thermodynamic measurement of the entropy suppression associated with the formation of the Kondo singlet, using temperature-dependent charge sensing and a Maxwell relation to track the suppression of spin entropy as the first electron is added to a strongly-coupled GaAs quantum dot. Plotting dN/dTdN/dTdN/dT against the simultaneously measured occupation NNN reveals an asymmetric lineshape with its peak shifted to N>1/2N>1/2N>1/2---a hallmark of Kondo screening---that weakens with increasing temperature and is qualitatively reproduced by numerical renormalization group (NRG) calculations, with a small but persistent offset to lower occupation relative to the theory. An independent measurement of conductance versus occupation on the same device provides a test of these quantities through the mixed-valence crossover and matches NRG within experimental uncertainty.
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.