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arXiv:0811.2677 · Physical Review B

Kondo cloud mediated long-range entanglement after local quench in a spin chain

Pasquale Sodano, Abolfazl Bayat, Sougato Bose

Published Mar 24, 2010• 48 citations
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Abstract

We show that, in the gapless Kondo regime, a single local quench at one end of a Kondo spin chain induces a fast and long-lived oscillatory dynamics. This quickly establishes a high-quality entanglement between the spins at the opposite ends of the chain. This entanglement is mediated by the Kondo cloud, attains a constant high value independent of the length for large chains, and shows thermal robustness. In contrast, when the Kondo cloud is absent, e.g., in the gapped dimer regime, only finite-size end to end effects can create some entanglement on a much longer time scale for rather short chains. By decoupling one end of the chain during the dynamics, one can distinguish between this end-end effect which vanishes, and the global Kondo cloud mediated entanglement, which persists. This quench approach paves the way to detect the elusive Kondo cloud through the entanglement between two individual spins. Our results show that nonperturbative cooperative phenomena from condensed matter may be exploited for quantum information.

DOI
10.1103/physrevb.81.100412

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We show that, in the gapless Kondo regime, a single local quench at one end of a Kondo spin chain induces a fast and long-lived oscillatory dynamics. This quickly establishes a high-quality entanglement between the spins at the opposite ends of the chain. This entanglement is mediated by the Kondo cloud, attains a constant high value independent of the length for large chains, and shows thermal robustness. In contrast, when the Kondo cloud is absent, e.g., in the gapped dimer regime, only finite-size end to end effects can create some entanglement on a much longer time scale for rather short chains. By decoupling one end of the chain during the dynamics, one can distinguish between this end-end effect which vanishes, and the global Kondo cloud mediated entanglement, which persists. This quench approach paves the way to detect the elusive Kondo cloud through the entanglement between two individual spins. Our results show that nonperturbative cooperative phenomena from condensed matter may be exploited for quantum information.
We exploit the unique features of the entanglement in the gapless Kondo regime to show that a single local quench at one end of a Kondo spin chain may always induce fast and long lived oscillatory dynamics, which establishes a high quality entanglement between the individual spins at the opposite ends of the chain. This entanglement is a footprint of the presence of the Kondo cloud and may be engineered so as to attain — even for very large chains- a constant high value independent of the length; in addition, it is thermally robust. To better evidence the remarkable peculiarities of the Kondo regime, we carry a parallel analysis of the entanglement properties of the Kondo spin chain model in the gapped dimerised regime where these remarkable features are absent.
We investigate the entanglement properties of the Kondo spin chain when it is prepared in its ground state as well as its dynamics following a single bond quench. We show that a true measure of entanglement such as negativity enables to characterize the unique features of the gapless Kondo regime. We determine the spatial extent of the Kondo screening cloud and propose an ansatz for the ground state in the Kondo regime accessible to this spin chain; we also demonstrate that the impurity spin is indeed maximally entangled with the Kondo cloud. We exploit these features of the entanglement in the gapless Kondo regime to show that a single local quench at one end of a Kondo spin chain may always induce a fast and long lived oscillatory dynamics, which establishes a high quality entanglement between the individual spins at the opposite ends of the chain. This entanglement is a footprint of the presence of the Kondo cloud and may be engineered so as to attain - even for very large chains- a constant high value independent of the length; in addition, it is thermally robust. To better evidence the remarkable peculiarities of the Kondo regime, we carry a parallel analysis of the entanglement properties of the Kondo spin chain model in the gapped dimerised regime where these remarkable features are absent.
We study the entanglement of an impurity at one end of a spin chain with a block of spins using negativity as a true measure of entanglement to characterize the unique features of the gapless Kondo regime in the spin-chain Kondo model. For this spin chain in the Kondo regime we determine---with a true entanglement measure---the spatial extent of the Kondo screening cloud, we propose an ansatz for its ground state and demonstrate that the impurity spin is indeed maximally entangled with the cloud. To better evidence the peculiarities of the Kondo regime, we carry a parallel analysis of the entanglement properties of the Kondo spin-chain model in the gapped dimerized regime. Our study shows how a genuine entanglement measure stemming from quantum information theory can fully characterize also nonperturbative regimes accessible to certain condensed matter systems.
This thesis investigates the properties of entanglement in one-dimensional many-body systems. In the first part, the non-equilibrium dynamics following a sudden global quench are exploited for the purpose of generating long-range entanglement. A number of initial states are considered. It is shown that the dynamics following the considered quench can be mapped to the problem of a state transfer. The quench can then be optimised by exploiting the literature about quantum state transfer to generate maximal long-range entanglement and maximal block entropy. \nIn the second part of the thesis, a spin chain emulation of the two-channel, Kondo (2CK) model is proposed. Studying the local magnetisation and susceptibility we show that the spin-only emulation truly represent the two-channel Kondo model and extract the Kondo temperature. A detailed entanglement analysis is presented. Using density matrix renormalisation group (DMRG), which allow for real space analysis, Kondo temperature and Kondo length are evaluated. An entanglement measure, namely the negativity, as well as the Schmidt gap are used as possible order parameters predicting the critical point. An extensive analysis of the block entropy of the system is presented for different limiting values of Kondo coupling. A universal scaling of the impurity contribution to the entropy is found and the 2CK residual entropy is extracted. \nThe last part explores quench dynamics in Kondo systems using time-dependent DMRG. For a quench in the Kondo coupling a travelling and breathing clouds are ob-served. A measurement-induced dynamics lead to an oscillation between an effective singlet and triplet states of the impurity and the Kondo cloud. Kondo temperature can be extracted from the frequency of the oscillation.
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 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.