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 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 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 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 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.
Abstract The screening of an impurity spin in the Kondo model occurs over a characteristic length scale ξ K , that defines the size of the Kondo screening cloud or ‘mist’. The presence of such a length scale in experimental and numerical results is rather subtle. A consistent way to show the presence of the screening cloud is to demonstrate scaling in the spatial correlations in terms of the single variable, r / ξ K instead of the correlations depending on r and ξ K separately. Here we study the paradigmatic one channel Kondo model using a spin chain representation, with an impurity spin at one end of the chain coupled with a strength J K ′ . Using Fermi liquid theory combined with numerical results, we obtain new high precision estimates of the non-universal terms in the entanglement entropy which leads to a verification of the expected non-integer ground-state degeneracy, g. This then allows us to study the impurity contribution to the entanglement in detail. If the impurity coupling J K ′ is varied, a precise determination of ξ K can then be obtained. The length scale, ξ K , is then shown to characterize the scaling of both the uniform and alternating part of a measure of the magnetization of part of an odd length chain.
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.
Entanglement in J 1 – J 2 , S = 1/2 quantum spin chains with an impurity is studied using analytic methods as well as large scale numerical density matrix renormalization group methods. The entanglement is investigated in terms of the von Neumann entropy, S = −Trρ A logρ A , for a subsystem A of size r of the chain. The impurity contribution to the uniform part of the entanglement entropy, S imp , is defined and analysed in detail in both the gapless, J 2 ≤ J 2 c , as well as the dimerized phase, J 2 > J 2 c , of the model. This quantum impurity model is in the universality class of the single channel Kondo model and it is shown that in a quite universal way the presence of the impurity in the gapless phase, J 2 ≤ J 2 c , gives rise to a large length scale, ξ K , associated with the screening of the impurity, the size of the Kondo screening cloud. The universality of Kondo physics then implies scaling of the form S imp ( r /ξ K , r / R ) for a system of size R . Numerical results are presented clearly demonstrating this scaling. At the critical point, J 2 c , an analytic approach based on a Fermi liquid picture, valid at distances and energy scales , is developed and analytic results at T = 0 are obtained showing S imp = πξ K [1+π(1− r / R )cot(π r / R )]/(12 R ) for finite R . For T >0, in the thermodynamic limit, we find S imp = [π 2 ξ K T /(6 v )]coth(2π rT / v ), with v the spin-wave velocity. In the dimerized phase an appealing picture of the entanglement is developed in terms of a thin soliton (TS) ansatz and the notions of impurity valence bonds (IVB) and single particle entanglement (SPE) are introduced. The TS-ansatz permits a variational calculation of the complete entanglement in the dimerized phase that appears to be exact in the thermodynamic limit at the Majumdar–Ghosh point, J 2 = J 1 /2, and surprisingly precise even close to the critical point J 2 c . In the appendices the TS-ansatz is further used to calculate and with high precision at the Majumdar–Ghosh point and the relation between the finite temperature entanglement entropy, S ( T ), and the thermal entropy, S th ( T ), is discussed. Finally, the alternating part of S imp is discussed, together with its relation to the boundary induced dimerization.