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arXiv:2601.11449 · Physical Review Research

Pathway to Kondo physics in quantum wires coupled to a repulsive spin impurity and manifestations in ytterbium atoms

Jeff Maki, Lidia Stocker, Oded Zilberberg

Published May 3, 2026• 0 citations
arXivHTMLPDF

Abstract

The Kondo effect is a paradigmatic model of strongly correlated physics, where a magnetic impurity forms a many-body singlet with a fermionic environment. The properties of this singlet depend sensitively on correlations within the environment, which are particularly pronounced in one dimension, where interactions give rise to Luttinger liquid behavior. A promising platform to study these effects is provided by cold gases of ytterbium (Yb) atoms, where an atomic impurity is coupled to an interacting one-dimensional fermionic environment via both magnetic and potential scattering. These two scattering mechanisms compete with each other, raising the question of how robust Kondo screening remains in such systems. Here, we show that potential scattering can suppress Kondo screening in one-dimensional Yb gases. Remarkably, however, Kondo physics persists in well-defined regimes determined by the interactions in the environment. Combining analytical renormalization-group methods with density-matrix renormalization-group simulations, we identify a transition from a strongly to a weakly entangled impurity as potential scattering increases. The two approaches are in excellent agreement across the parameter regimes considered. Our results provide a quantitative criterion for the emergence of Kondo screening in one-dimensional Yb gases and delineate experimentally accessible regimes for its realization in cold-atom platforms.

DOI
10.1103/ssdp-yqfn

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The Kondo effect is a paradigmatic model of strongly correlated physics, where a magnetic impurity forms a many-body singlet with a fermionic environment. The properties of this singlet depend sensitively on correlations within the environment, which are particularly pronounced in one dimension, where interactions give rise to Luttinger liquid behavior. A promising platform to study these effects is provided by cold gases of ytterbium (Yb) atoms, where an atomic impurity is coupled to an interacting one-dimensional fermionic environment via both magnetic and potential scattering. These two scattering mechanisms compete with each other, raising the question of how robust Kondo screening remains in such systems. Here, we show that potential scattering can suppress Kondo screening in one-dimensional Yb gases. Remarkably, however, Kondo physics persists in well-defined regimes determined by the interactions in the environment. Combining analytical renormalization-group methods with density-matrix renormalization-group simulations, we identify a transition from a strongly to a weakly entangled impurity as potential scattering increases. The two approaches are in excellent agreement across the parameter regimes considered. Our results provide a quantitative criterion for the emergence of Kondo screening in one-dimensional Yb gases and delineate experimentally accessible regimes for its realization in cold-atom platforms.
The quantum physics of one dimensional systems exhibits many remarkable and exotic physical phenomena. These are the result of the strong correlations which exist in such systems due to the reduced dimensionality and in many cases can be described by Luttinger Liquid theory. Likewise quantum impurity systems, where a bath of particles couples to the same impurity, exhibit well known non perturbative phenomena like the Kondo effect. In this thesis we study the physics of quantum impurities in interacting environments - the intersection of these two areas. Such Luttinger-impurity systems can be realized experimentally in a range of different settings from quantum wires and carbon nano tubes to edges of fractional quantum hall systems and cold atom gases. We show that many of the models used to describe these experiments are integrable and can be studied by means of the Bethe Ansatz. This powerful and exact method provides us with the exact eigenstates and energy levels of the model Hamiltonian. The models considered include two which describe a Lutttinger liquid coupled to a back scattering impurity, the Kane-Fisher and weak tunnelling model as well as Luttinger liquids coupled a quantum dot in various geometries: at the boundary, sidecoupled and embedded. To incorporate both the backscattering nature of the impurities and the interacting bulk particles a new formulation of the Bethe Ansatz is developed and implemented. The eigenstates and spectra of the models are found and used to investigate their ground state and thermodynamic properties.
The Kondo effect is a hallmark of strongly-correlated systems, where an impurity's local degrees of freedom are screened by conduction electrons, forming a many-body singlet. With increasing degrees of freedom in the impurity, theoretical studies face significant challenges in accurately identifying and characterizing the underlying mechanisms that screen the impurity. In this work, we introduce a straightforward yet powerful methodology for identifying the formation of Kondo singlets and their screening mechanisms, by utilizing the numerical renormalization group (NRG) combined with the matrix product states (MPS) technique. We demonstrate the effectiveness of our method on the single and two-level Anderson impurity models (AIM). Furthermore, we discuss potential generalizations of the method to multichannel and multiorbital Kondo impurities. Harnessing advanced tensor network techniques, our approach extends to complex impurity systems, offering a robust and versatile framework for studying Kondo physics.
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.
A magnetic moment in a metal or in a quantum dot is, at low temperatures, screened by the conduction electrons through the mechanism of the Kondo effect. This gives rise to spin-spin correlations between the magnetic moment and the conduction electrons, which can have a substantial spatial extension. We study this phenomenon, the so-called Kondo cloud, by means of the density matrix renormalization group method for the case of the single-impurity Anderson model. We focus on the question whether the Kondo screening length, typically assumed to be proportional to the inverse Kondo temperature, can be extracted from the spin-spin correlations. For several mechanisms---the gate potential and a magnetic field---which destroy the Kondo effect, we investigate the behavior of the screening cloud induced by these perturbations.
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 magnetic moment in a metal or in a quantum dot is, at low temperatures, screened by the conduction electrons through the mechanism of the Kondo effect. This gives rise to spin-spin correlations between the magnetic moment and the conduction electrons, which can have a substantial spatial extension. We study this phenomenon, the so-called Kondo cloud, by means of the density matrix renormalization group method for the case of the single-impurity Anderson model. We focus on the question whether the Kondo screening length, typically assumed to be proportional to the inverse Kondo temperature, can be extracted from the spin-spin correlations. For several mechanisms -- the gate potential and a magnetic field -- that destroy the Kondo effect, we investigate the behavior of the screening cloud induced by these perturbations.