Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2504.16308 · Physical review. B./Physical review. B

Nontrivial entanglement passively mediated by a quenched magnetic impurity

Adelina A. Orlandini, G. G. Blesio, C. J. Gazza, L. O. Manuel

Published Jul 28, 2025• 0 citations
arXivHTMLPDF

Abstract

We investigate the entanglement properties of a Kondo system undergoing a transition to a state with a quenched magnetic impurity, using the density matrix renormalization group method. We focus on a two-channel spin-1 Kondo impurity with single-ion anisotropy, where a quantum phase transition occurs between two topologically distinct local Fermi liquids. In the fully screened Kondo phase, realized at lower anisotropies, the entangled region surrounding the magnetic impurity mimics the Kondo screening cloud, although its length does not follow the conventional behavior. In contrast, beyond the transition, the system enters a non-Landau Fermi liquid phase with a markedly different entanglement structure: As the impurity is quenched and disentangled from the rest of the system due to the breakdown of the Kondo effect, the two conduction channels---coupled only through the impurity---develop a significant degree of entanglement with one another. Our findings demonstrate that a quenched magnetic impurity can passively and efficiently mediate entanglement between spatially separated conduction bands.

DOI
10.1103/kx2n-8rn8

Related papers

Kondo breakdown as an entanglement transition driven by continuous measurement

Debraj Debata, Abhirup Mukherjee, Siddhartha Lal

We study the breakdown of Kondo screening by a local magnetic field from the perspective of a measurement-driven entanglement transition in a monitored quantum system. Here, the Kondo coupling leads to the growth in entanglement of an impurity spin with it's fermionic environment, while the local field plays the role of a continuous observer. Using a non-perturbative Unitary Renormalization Group (URG) approach, we derive coupled renormalization-group flow equations for the Kondo exchange and the local field, and obtain a field-dependent RG phase diagram. The RG flows separate a low-energy Kondo-screened phase, where the impurity is absorbed into the Fermi sea and forms an entangled singlet with the conduction bath, from a polarized local-moment phase in which screening is frustrated and impurity-bath entanglement is suppressed. We identify the fixed-point Hamiltonians governing the two phases and the critical regime, and relate the transition to the emergence of a novel non-Fermi liquid. Various impurity signatures such as the spectral function and thermalisation of impurity observables are used to characterise this entanglement transition. These results offer insight into the interplay of decoherence and measurement in governing the dynamics of a prototypical quantum system.

cond-mat.str-elCross-listedarXiv:2602.20600•Feb 25, 2026•0 citations

Long-Range Entanglement near a Kondo-Destruction Quantum Critical Point

Christopher Wagner, Tathagata Chowdhury, J. H. Pixley +1 more

The numerical renormalization group is used to study quantum entanglement in the Kondo impurity model with a density of states ρ(ϵ)∝|ϵ|^{r} (0<r<1/2) that vanishes at the Fermi energy ϵ=0. This nonintegrable model features a Kondo-destruction quantum critical point (QCP) separating a partially screened phase from a local-moment phase. The impurity contribution S_{e}^{imp} to the entanglement entropy between a region of radius R around the magnetic impurity and the rest of the system reveals a length scale R^{*} that distinguishes a region R≪R^{*} of strong critical entanglement from one R≫R^{*} of weak entanglement. Within each phase, S_{e}^{imp} is a universal function of R/R^{*} with a power-law decay for R/R^{*}≫1. The entanglement length R^{*} diverges on approach to the interacting QCP, showing that the critical Kondo screening cloud subsumes the entire system as the impurity becomes maximally entangled with the conduction band. This work has implications for entanglement calculations in other models and for the nature of heavy-fermion quantum criticality.

arXiv:1803.07583•Physical Review Letters•Oct 5, 2018•19 citations

Hierarchical entanglement shells of multichannel Kondo clouds

Jeongmin Shim, Dong-Hoon Kim, H.-S. Sim

Impurities or boundaries often impose nontrivial boundary conditions on a gapless bulk, resulting in distinct boundary universality classes for a given bulk, phase transitions, and non-Fermi liquids in diverse systems. The underlying boundary states however remain largely unexplored. This is related with a fundamental issue how a Kondo cloud spatially forms to screen a magnetic impurity in a metal. Here we predict the quantum-coherent spatial and energy structure of multichannel Kondo clouds, representative boundary states involving competing non-Fermi liquids, by studying quantum entanglement between the impurity and the channels. Entanglement shells of distinct non-Fermi liquids coexist in the structure, depending on the channels. As temperature increases, the shells become suppressed one by one from the outside, and the remaining outermost shell determines the thermal phase of each channel. Detection of the entanglement shells is experimentally feasible. Our findings suggest a guide to studying other boundary states and boundary-bulk entanglement.

arXiv:2306.10583•Nature Communications•Jun 14, 2023•10 citations

Probing Impurity Quantum Criticality with Entanglement Witnesses

Mateo Cárdenes Wuttig, Andrew J. Millis

Entanglement is a defining feature of quantum mechanics, and its relation to quantum criticality is of considerable current interest. Here we show that measurable spin and charge fluctuations provide an entanglement witness of quantum criticality in the two-impurity Kondo model, which has experimental realizations in terms of coupled quantum dots and magnetic impurities added to surfaces. We use density-matrix renormalization group and numerical renormalization group calculations to resolve the non-Fermi-liquid critical point separating two independently Kondo-screened impurities from an inter-impurity singlet and interpret it as a change in the dominant entanglement partner of each local moment: from entanglement of the local moment with an extended set of conduction-electron degrees of freedom to entanglement with the other impurity. This reorganization is accompanied by a singular response of the impurity-bath entanglement and the inter-impurity susceptibility. We show how the same structure is encoded in the quantum Fisher information of collective spin and charge operators at zero and finite temperatures, connecting the entanglement picture to experimentally accessible dynamical response functions. Our results establish impurity systems as controlled settings in which quantum-critical entanglement can be detected through measurable correlations, and provide further insight into the possibility of understanding heavy-fermion physics in terms of entanglement.

cond-mat.str-elCross-listedarXiv:2608.12317•Aug 13, 2026•0 citations

Impurity entanglement entropy and the Kondo screening cloud

Erik Schwartz Sørensen, Ming-Shyang Chang, Nicolas Laflorencie +1 more

The screening of an impurity spin by conduction electrons is associated with the formation of a large Kondo screening cloud, of size ξ K . We study the quantum entanglement between a region of size r surrounding the impurity and the rest of the sample (of total size R ) using density matrix renormalization group and analytic methods. The corresponding ‘impurity entanglement entropy’, S imp , is shown to be a universal scaling function of r /ξ K and r / R . We calculate this universal function using Fermi liquid theory in the regime ξ K ≪ r .

arXiv:cond-mat/0606705•Journal of Statistical Mechanics Theory and Experiment•Jan 5, 2007•52 citations

Quantum phase transition of Ising-coupled Kondo impurities

Markus Garst, Stefan K. Kehrein, Thomas Pruschke +2 more

We investigate a model of two Kondo impurities coupled via an Ising interaction. Exploiting the mapping to a generalized single-impurity Anderson model, we establish that the model has a singlet and a (pseudospin) doublet phase separated by a Kosterlitz-Thouless quantum phase transition. Based on a strong-coupling analysis and renormalization-group arguments, we show that at this transition the conductance $G$ through the system either displays a zero-bias anomaly, $G\ensuremath{\sim}{\ensuremath{\mid}V\ensuremath{\mid}}^{\ensuremath{-}2(\sqrt{2}\ensuremath{-}1)}$, or takes a universal value, $G=({e}^{2}∕\ensuremath{\pi}\ensuremath{\hbar}){\mathrm{cos}}^{2}(\ensuremath{\pi}∕2\sqrt{2})$, depending on the experimental setup. Close to the Toulouse point of the individual Kondo impurities, the strong-coupling analysis allows us to obtain the location of the phase boundary analytically. For general model parameters, we determine the phase diagram and investigate the thermodynamics using numerical renormalization-group calculations. In the singlet phase close to the quantum phase transition, the entropy is quenched in two steps: first the two Ising-coupled spins form a magnetic minidomain which is, in a second step, screened by a Kondoesque collective resonance in an effective solitonic Fermi sea. In addition, we present a flow-equation analysis which provides a different mapping of the two-impurity model to a generalized single-impurity Anderson model in terms of fully renormalized couplings, which is applicable for the whole range of model parameters.

arXiv:cond-mat/0310222•Physical Review B•Jun 18, 2004•52 citations
We investigate the entanglement properties of a Kondo system undergoing a transition to a state with a quenched magnetic impurity, using the density matrix renormalization group method. We focus on a two-channel spin-1 Kondo impurity with single-ion anisotropy, where a quantum phase transition occurs between two topologically distinct local Fermi liquids. In the fully screened Kondo phase, realized at lower anisotropies, the entangled region surrounding the magnetic impurity mimics the Kondo screening cloud, although its length does not follow the conventional behavior. In contrast, beyond the transition, the system enters a non-Landau Fermi liquid phase with a markedly different entanglement structure: As the impurity is quenched and disentangled from the rest of the system due to the breakdown of the Kondo effect, the two conduction channels---coupled only through the impurity---develop a significant degree of entanglement with one another. Our findings demonstrate that a quenched magnetic impurity can passively and efficiently mediate entanglement between spatially separated conduction bands.
We study the breakdown of Kondo screening by a local magnetic field from the perspective of a measurement-driven entanglement transition in a monitored quantum system. Here, the Kondo coupling leads to the growth in entanglement of an impurity spin with it's fermionic environment, while the local field plays the role of a continuous observer. Using a non-perturbative Unitary Renormalization Group (URG) approach, we derive coupled renormalization-group flow equations for the Kondo exchange and the local field, and obtain a field-dependent RG phase diagram. The RG flows separate a low-energy Kondo-screened phase, where the impurity is absorbed into the Fermi sea and forms an entangled singlet with the conduction bath, from a polarized local-moment phase in which screening is frustrated and impurity-bath entanglement is suppressed. We identify the fixed-point Hamiltonians governing the two phases and the critical regime, and relate the transition to the emergence of a novel non-Fermi liquid. Various impurity signatures such as the spectral function and thermalisation of impurity observables are used to characterise this entanglement transition. These results offer insight into the interplay of decoherence and measurement in governing the dynamics of a prototypical quantum system.
The numerical renormalization group is used to study quantum entanglement in the Kondo impurity model with a density of states ρ(ϵ)∝|ϵ|^{r} (0<r<1/2) that vanishes at the Fermi energy ϵ=0. This nonintegrable model features a Kondo-destruction quantum critical point (QCP) separating a partially screened phase from a local-moment phase. The impurity contribution S_{e}^{imp} to the entanglement entropy between a region of radius R around the magnetic impurity and the rest of the system reveals a length scale R^{*} that distinguishes a region R≪R^{*} of strong critical entanglement from one R≫R^{*} of weak entanglement. Within each phase, S_{e}^{imp} is a universal function of R/R^{*} with a power-law decay for R/R^{*}≫1. The entanglement length R^{*} diverges on approach to the interacting QCP, showing that the critical Kondo screening cloud subsumes the entire system as the impurity becomes maximally entangled with the conduction band. This work has implications for entanglement calculations in other models and for the nature of heavy-fermion quantum criticality.
Impurities or boundaries often impose nontrivial boundary conditions on a gapless bulk, resulting in distinct boundary universality classes for a given bulk, phase transitions, and non-Fermi liquids in diverse systems. The underlying boundary states however remain largely unexplored. This is related with a fundamental issue how a Kondo cloud spatially forms to screen a magnetic impurity in a metal. Here we predict the quantum-coherent spatial and energy structure of multichannel Kondo clouds, representative boundary states involving competing non-Fermi liquids, by studying quantum entanglement between the impurity and the channels. Entanglement shells of distinct non-Fermi liquids coexist in the structure, depending on the channels. As temperature increases, the shells become suppressed one by one from the outside, and the remaining outermost shell determines the thermal phase of each channel. Detection of the entanglement shells is experimentally feasible. Our findings suggest a guide to studying other boundary states and boundary-bulk entanglement.
Entanglement is a defining feature of quantum mechanics, and its relation to quantum criticality is of considerable current interest. Here we show that measurable spin and charge fluctuations provide an entanglement witness of quantum criticality in the two-impurity Kondo model, which has experimental realizations in terms of coupled quantum dots and magnetic impurities added to surfaces. We use density-matrix renormalization group and numerical renormalization group calculations to resolve the non-Fermi-liquid critical point separating two independently Kondo-screened impurities from an inter-impurity singlet and interpret it as a change in the dominant entanglement partner of each local moment: from entanglement of the local moment with an extended set of conduction-electron degrees of freedom to entanglement with the other impurity. This reorganization is accompanied by a singular response of the impurity-bath entanglement and the inter-impurity susceptibility. We show how the same structure is encoded in the quantum Fisher information of collective spin and charge operators at zero and finite temperatures, connecting the entanglement picture to experimentally accessible dynamical response functions. Our results establish impurity systems as controlled settings in which quantum-critical entanglement can be detected through measurable correlations, and provide further insight into the possibility of understanding heavy-fermion physics in terms of entanglement.
The screening of an impurity spin by conduction electrons is associated with the formation of a large Kondo screening cloud, of size ξ K . We study the quantum entanglement between a region of size r surrounding the impurity and the rest of the sample (of total size R ) using density matrix renormalization group and analytic methods. The corresponding ‘impurity entanglement entropy’, S imp , is shown to be a universal scaling function of r /ξ K and r / R . We calculate this universal function using Fermi liquid theory in the regime ξ K ≪ r .
We investigate a model of two Kondo impurities coupled via an Ising interaction. Exploiting the mapping to a generalized single-impurity Anderson model, we establish that the model has a singlet and a (pseudospin) doublet phase separated by a Kosterlitz-Thouless quantum phase transition. Based on a strong-coupling analysis and renormalization-group arguments, we show that at this transition the conductance GGG through the system either displays a zero-bias anomaly, $G\ensuremath{\sim}{\ensuremath{\mid}V\ensuremath{\mid}}^{\ensuremath{-}2(\sqrt{2}\ensuremath{-}1)}$, or takes a universal value, $G=({e}^{2}∕\ensuremath{\pi}\ensuremath{\hbar}){\mathrm{cos}}^{2}(\ensuremath{\pi}∕2\sqrt{2})$, depending on the experimental setup. Close to the Toulouse point of the individual Kondo impurities, the strong-coupling analysis allows us to obtain the location of the phase boundary analytically. For general model parameters, we determine the phase diagram and investigate the thermodynamics using numerical renormalization-group calculations. In the singlet phase close to the quantum phase transition, the entropy is quenched in two steps: first the two Ising-coupled spins form a magnetic minidomain which is, in a second step, screened by a Kondoesque collective resonance in an effective solitonic Fermi sea. In addition, we present a flow-equation analysis which provides a different mapping of the two-impurity model to a generalized single-impurity Anderson model in terms of fully renormalized couplings, which is applicable for the whole range of model parameters.