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

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.

Figure 1

(Color online) Comparing the Kondo $\left(J_2=0\right)$ and the dimer $\left(J_2=0.42\right)$ regimes. (a) Entanglement vs time for $N=30$ with $J^{\prime }=0.19$ for the KR (solid line) and $J^{\prime }=0.44$ for the DR (dashed line). (b) $E_m$ vs the length $N$. (c) $t_{opt}$ vs $N$. (d) $J_{opt}^{\prime }$ vs length $N$.

Figure 2

(Color online) (a) $t_{opt}$ vs $1/\sqrt{J_{opt}^{\prime }}$ in the KR. (b) $E_m$ at $t\propto 1/J_{opt}^{\prime }$ vs $J_2$ for chains of different lengths. (c) Entanglement attained at $t_{opt}$ vs $J^{\prime }$ for Kondo and DRs for $N=20$. (d) $E_m$ vs temperature after bond quenching (blue line) and induced by (static) weak coupling with the rest of the chain (red line) for a chain of $N=10$.

Figure 3

(Color online) (a) Different $|G{S}_I⟩$ for entanglement generation through quench dynamics. Top: the ground states with $\xi <N/2$ (no entanglement). Middle: $N/2<\xi <N-2$ (some entanglement). Bottom: $\xi =N-2$ (optimal entanglement). (b) Decoupling the impurity from the chain.

Figure 4

(Color online) $E_m$ vs $N$ after decoupling the first impurity.