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:1212.3963 · Physical Review B

Spin-spin correlations between two Kondo impurities coupled to an open Hubbard chain

Alexander C. Tiegel, Piet E. Dargel, K. Hallberg, Holger Frahm, Thomas Pruschke

Published Feb 19, 2013• 4 citations
arXivHTMLPDF

Abstract

In order to study the interplay between Kondo and Ruderman-Kittel-Kasuya-Yosida interaction, we calculate the spin-spin correlation functions between two Kondo impurities coupled to different sites of a half-filled open Hubbard chain. Using the density-matrix renormalization group (DMRG), we reexamine the exponents for the power-law decay of the correlation function between the two impurity spins as a function of the antiferromagnetic coupling $J$, the Hubbard interaction $U$, and the distance $R$ between the impurities. The exponents for finite systems obtained in this work deviate from previously published DMRG calculations. We furthermore show that the long-distance behavior of the exponents is the same for impurities coupled to the bulk or to both ends of the chain. We note that a universal exponent for the asymptotic behavior can not be extracted from these finite-size systems with open boundary conditions.

DOI
10.1103/physrevb.87.075122

Related papers

Equilibrium and real-time properties of the spin correlation function in the two-impurity Kondo model

Benedikt Lechtenberg, Frithjof B. Anders

We investigate the equilibrium and real-time properties of the spin-correlation function $\ensuremath{\langle}{\stackrel{P\vec}{S}}_{1}{\stackrel{P\vec}{S}}_{2}\ensuremath{\rangle}$ in the two-impurity Kondo model for different distances $R$ between the two-impurity spins. It is shown that the competition between the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction and the Kondo effect governs the amplitude of $\ensuremath{\langle}{\stackrel{P\vec}{S}}_{1}{\stackrel{P\vec}{S}}_{2}\ensuremath{\rangle}$. For distances $R$ exceeding the Kondo length scale, the Kondo effect also has a profound effect on the sign of the correlation function. For ferromagnetic Heisenberg couplings $J$ between the impurities and the conduction band, the Kondo effect is absent and the correlation function only decays for distances beyond a certain length scale introduced by finite temperature. The real-time dynamics after a sudden quench of the system reveals that correlations propagate through the conduction band with Fermi velocity. We identify two distinct timescales for the long-time behavior, which reflects that for small $J$ the system is driven by the RKKY interaction while for large $J$ the Kondo effect dominates. Interestingly, we find that at certain distances a one-dimensional dispersion obeying $\ensuremath{\epsilon}(k)=\ensuremath{\epsilon}(\ensuremath{-}k)$ may lead to a local parity conservation of the impurities such that $\ensuremath{\langle}{\stackrel{P\vec}{S}}_{1}{\stackrel{P\vec}{S}}_{2}\ensuremath{\rangle}$ becomes a conserved quantity for long times and does not decay to its equilibrium value.

arXiv:1805.04254•Physical review. B./Physical review. B•Jul 6, 2018•5 citations

Entanglement Probe of Two-Impurity Kondo Physics in a Spin Chain

Abolfazl Bayat, Sougato Bose, Pasquale Sodano +1 more

We propose that real-space properties of the two-impurity Kondo model can be obtained from an effective spin model where two single-impurity Kondo spin chains are joined via an Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between the two impurity spins. We then use a density matrix renormalization group approach, valid in all ranges of parameters, to study its features using two complementary quantum-entanglement measures, the negativity and the von Neumann entropy. This nonperturbative approach enables us to uncover the precise dependence of the spatial extent ξ(K) of the Kondo screening cloud with the Kondo and RKKY couplings. Our results reveal an exponential suppression of the Kondo temperature T(K)~1/ξ(K) with the size of the effective impurity spin in the limit of large ferromagnetic RKKY coupling, a striking display of "Kondo resonance narrowing" in the two-impurity Kondo model. We also show how the antiferromagnetic RKKY interaction produces an effective decoupling of the impurities from the bulk already for intermediate strengths of this interaction, and, furthermore, exhibit how the non-Fermi liquid quantum critical point is signaled in the quantum entanglement between various parts of the system.

arXiv:1201.6668•Physical Review Letters•Aug 7, 2012•99 citations

Spin correlations in dense Kondo systems

Paolo Maria Santini, Jenő Sólyom, Lucio Claudio Andreani +1 more

We performed numerical diagonalization studies of the periodic Anderson Model on finite chains up to 6 sites, in the integral valence limit for T=0. We find that in the weak coupling (Kondo) region the hybridization between f and conduction electrons induces pronounced correlations between the f spins. These correlations are ferromagnetic for low filling and become antiferromagnetic close to half-filling, with a smooth transition between the limiting cases. In no limit can the physics be completely described by a Ruderman–Kittel–Kasuya–Yosida effective spin Hamiltonian, as f and conduction band electrons are always correlated. To study the onset of long range order we considered also a simpler model for the half-filled case, called ‘‘Kondo necklace.’’ We studied the model at T=0 by numerical diagonalization and finite-size scaling, on chains up to 12 sites. We find that below a finite critical value of the Kondo coupling there exists a gapless phase with quasi long range antiferromagnetic correlations.

Journal of Applied Physics•May 15, 1993•1 citation

Kondo effect in XXZ spin chains

Akira Furusaki, Takashi Hikihara

The Kondo effect in a one-dimensional spin-$\frac{1}{2}$ $\mathrm{XXZ}$ model in the gapless $\mathrm{XY}$ regime $(\ensuremath{-}1<\ensuremath{\Delta}<~1)$ is studied both analytically and numerically. In our model an impurity spin $(S=1/2)$ is coupled to a single spin in the $\mathrm{XXZ}$ spin chain. Perturbative renormalization-group (RG) analysis is performed for various limiting cases to deduce low-energy fixed points. It is shown that in the ground state the impurity spin is screened by forming a singlet with a spin in the host $\mathrm{XXZ}$ chain. In the antiferromagnetic side $(0<\ensuremath{\Delta}<~1)$ the host chain is cut into two semi-infinite chains by the singlet. In the ferromagnetic side $(\ensuremath{-}1<\ensuremath{\Delta}<0),$ on the other hand, the host $\mathrm{XXZ}$ chain remains as a single chain through ``healing'' of a weakened bond in the low-energy (long-distance) limit. The density-matrix renormalization-group method is used to study the size scaling of finite-size energy gaps and the power-law decay of correlation functions in the ground state. The numerical results are in good agreement with the predictions of the RG analysis. Low-temperature behaviors of specific heat and susceptibility are also discussed.

arXiv:cond-mat/9802258•Physical review. B, Condensed matter•Sep 1, 1998•25 citations

Anderson impurity in the one-dimensional Hubbard model for finite-size systems

S. Costamagna, C. J. Gazza, M. E. Torio +1 more

An Anderson impurity in a Hubbard model on chains with finite length is studied using the density-matrix renormalization-group (DMRG) technique. In the first place, we analyzed how the reduction of electron density from half filling to quarter filling affects the Kondo resonance in the limit of Hubbard repulsion $U=0$. In general, a weak dependence with the electron density was found for the local density of states (LDOS), at the impurity except when the impurity, at half filling, is close to a mixed-valence regime. Next, in the central part of this paper, we studied the effects of finite Hubbard interaction on the chain at quarter filling. Our main result is that this interaction drives the impurity into a more defined Kondo regime although accompanied in most cases by a reduction of the spectral weight of the impurity LDOS. Again, for the impurity in the mixed-valence regime, we observed an interesting nonmonotonic behavior. We also concluded that the conductance, computed for a small finite bias applied to the leads, follows the behavior of the impurity LDOS, as in the case of noninteracting chains. Finally, we analyzed how the Hubbard interaction and the finite chain length affect the spin compensation cloud both at zero and at finite temperature, in this case using quantum Monte Carlo techniques.

arXiv:cond-mat/0608725•Physical Review B•Nov 6, 2006•25 citations

Quantum correlations in nanostructured two-impurity Kondo systems

Marco Nizama, Diego Frustaglia, K. Hallberg

We study the ground-state entanglement properties of nanostructured Kondo systems consisting of a pair of impurity spins coupled to a background of confined electrons. The competition between the Ruderman-Kittel-Kasuya-Yosida-like coupling and the Kondo effect determines the development of quantum correlations between the different parts of the system. A key element is the electronic filling due to confinement. An even electronic filling leads to results similar to those found previously for extended systems, where the properties of the reduced impurity spin subsystem are uniquely determined by the spin-correlation function defining a one-dimensional phase space. An odd filling, instead, breaks spin rotation symmetry unfolding a two-dimensional phase space showing rich entanglement characteristics as, e.g., the requirement of a larger amount of entanglement for the development of nonlocal correlations between impurity spins. We illustrate these results by numerical simulations of elliptic quantum corrals with magnetic impurities at the foci as a case study.

arXiv:1205.4393•Physical Review B•Aug 6, 2012•7 citations
In order to study the interplay between Kondo and Ruderman-Kittel-Kasuya-Yosida interaction, we calculate the spin-spin correlation functions between two Kondo impurities coupled to different sites of a half-filled open Hubbard chain. Using the density-matrix renormalization group (DMRG), we reexamine the exponents for the power-law decay of the correlation function between the two impurity spins as a function of the antiferromagnetic coupling JJJ, the Hubbard interaction UUU, and the distance RRR between the impurities. The exponents for finite systems obtained in this work deviate from previously published DMRG calculations. We furthermore show that the long-distance behavior of the exponents is the same for impurities coupled to the bulk or to both ends of the chain. We note that a universal exponent for the asymptotic behavior can not be extracted from these finite-size systems with open boundary conditions.
We investigate the equilibrium and real-time properties of the spin-correlation function $\ensuremath{\langle}{\stackrel{P\vec}{S}}_{1}{\stackrel{P\vec}{S}}_{2}\ensuremath{\rangle}$ in the two-impurity Kondo model for different distances RRR between the two-impurity spins. It is shown that the competition between the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction and the Kondo effect governs the amplitude of $\ensuremath{\langle}{\stackrel{P\vec}{S}}_{1}{\stackrel{P\vec}{S}}_{2}\ensuremath{\rangle}$. For distances RRR exceeding the Kondo length scale, the Kondo effect also has a profound effect on the sign of the correlation function. For ferromagnetic Heisenberg couplings JJJ between the impurities and the conduction band, the Kondo effect is absent and the correlation function only decays for distances beyond a certain length scale introduced by finite temperature. The real-time dynamics after a sudden quench of the system reveals that correlations propagate through the conduction band with Fermi velocity. We identify two distinct timescales for the long-time behavior, which reflects that for small JJJ the system is driven by the RKKY interaction while for large JJJ the Kondo effect dominates. Interestingly, we find that at certain distances a one-dimensional dispersion obeying $\ensuremath{\epsilon}(k)=\ensuremath{\epsilon}(\ensuremath{-}k)$ may lead to a local parity conservation of the impurities such that $\ensuremath{\langle}{\stackrel{P\vec}{S}}_{1}{\stackrel{P\vec}{S}}_{2}\ensuremath{\rangle}$ becomes a conserved quantity for long times and does not decay to its equilibrium value.
We propose that real-space properties of the two-impurity Kondo model can be obtained from an effective spin model where two single-impurity Kondo spin chains are joined via an Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between the two impurity spins. We then use a density matrix renormalization group approach, valid in all ranges of parameters, to study its features using two complementary quantum-entanglement measures, the negativity and the von Neumann entropy. This nonperturbative approach enables us to uncover the precise dependence of the spatial extent ξ(K) of the Kondo screening cloud with the Kondo and RKKY couplings. Our results reveal an exponential suppression of the Kondo temperature T(K)~1/ξ(K) with the size of the effective impurity spin in the limit of large ferromagnetic RKKY coupling, a striking display of "Kondo resonance narrowing" in the two-impurity Kondo model. We also show how the antiferromagnetic RKKY interaction produces an effective decoupling of the impurities from the bulk already for intermediate strengths of this interaction, and, furthermore, exhibit how the non-Fermi liquid quantum critical point is signaled in the quantum entanglement between various parts of the system.
We performed numerical diagonalization studies of the periodic Anderson Model on finite chains up to 6 sites, in the integral valence limit for T=0. We find that in the weak coupling (Kondo) region the hybridization between f and conduction electrons induces pronounced correlations between the f spins. These correlations are ferromagnetic for low filling and become antiferromagnetic close to half-filling, with a smooth transition between the limiting cases. In no limit can the physics be completely described by a Ruderman–Kittel–Kasuya–Yosida effective spin Hamiltonian, as f and conduction band electrons are always correlated. To study the onset of long range order we considered also a simpler model for the half-filled case, called ‘‘Kondo necklace.’’ We studied the model at T=0 by numerical diagonalization and finite-size scaling, on chains up to 12 sites. We find that below a finite critical value of the Kondo coupling there exists a gapless phase with quasi long range antiferromagnetic correlations.
The Kondo effect in a one-dimensional spin-12\frac{1}{2}21​ XXZ\mathrm{XXZ}XXZ model in the gapless XY\mathrm{XY}XY regime $(\ensuremath{-}1<\ensuremath{\Delta}<~1)$ is studied both analytically and numerically. In our model an impurity spin (S=1/2)(S=1/2)(S=1/2) is coupled to a single spin in the XXZ\mathrm{XXZ}XXZ spin chain. Perturbative renormalization-group (RG) analysis is performed for various limiting cases to deduce low-energy fixed points. It is shown that in the ground state the impurity spin is screened by forming a singlet with a spin in the host XXZ\mathrm{XXZ}XXZ chain. In the antiferromagnetic side $(0<\ensuremath{\Delta}<~1)$ the host chain is cut into two semi-infinite chains by the singlet. In the ferromagnetic side $(\ensuremath{-}1<\ensuremath{\Delta}<0),$ on the other hand, the host XXZ\mathrm{XXZ}XXZ chain remains as a single chain through ``healing'' of a weakened bond in the low-energy (long-distance) limit. The density-matrix renormalization-group method is used to study the size scaling of finite-size energy gaps and the power-law decay of correlation functions in the ground state. The numerical results are in good agreement with the predictions of the RG analysis. Low-temperature behaviors of specific heat and susceptibility are also discussed.
An Anderson impurity in a Hubbard model on chains with finite length is studied using the density-matrix renormalization-group (DMRG) technique. In the first place, we analyzed how the reduction of electron density from half filling to quarter filling affects the Kondo resonance in the limit of Hubbard repulsion U=0U=0U=0. In general, a weak dependence with the electron density was found for the local density of states (LDOS), at the impurity except when the impurity, at half filling, is close to a mixed-valence regime. Next, in the central part of this paper, we studied the effects of finite Hubbard interaction on the chain at quarter filling. Our main result is that this interaction drives the impurity into a more defined Kondo regime although accompanied in most cases by a reduction of the spectral weight of the impurity LDOS. Again, for the impurity in the mixed-valence regime, we observed an interesting nonmonotonic behavior. We also concluded that the conductance, computed for a small finite bias applied to the leads, follows the behavior of the impurity LDOS, as in the case of noninteracting chains. Finally, we analyzed how the Hubbard interaction and the finite chain length affect the spin compensation cloud both at zero and at finite temperature, in this case using quantum Monte Carlo techniques.
We study the ground-state entanglement properties of nanostructured Kondo systems consisting of a pair of impurity spins coupled to a background of confined electrons. The competition between the Ruderman-Kittel-Kasuya-Yosida-like coupling and the Kondo effect determines the development of quantum correlations between the different parts of the system. A key element is the electronic filling due to confinement. An even electronic filling leads to results similar to those found previously for extended systems, where the properties of the reduced impurity spin subsystem are uniquely determined by the spin-correlation function defining a one-dimensional phase space. An odd filling, instead, breaks spin rotation symmetry unfolding a two-dimensional phase space showing rich entanglement characteristics as, e.g., the requirement of a larger amount of entanglement for the development of nonlocal correlations between impurity spins. We illustrate these results by numerical simulations of elliptic quantum corrals with magnetic impurities at the foci as a case study.