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Entanglement in the Kondo Spin Chain

This talk explores quantum information in condensed matter, focusing on Kondo physics and entanglement in the Kondo ground state. It discusses generating long-range entanglement in gapped and gapless systems, emphasizing the exponential decay in intrinsic length scales for the former and algebraic correlations decay in the latter. The Kondo Spin Chain's correlations decay exponentially despite being gapless. The discussion includes the Kondo phase, dimer phase, local quench, and optimal parameters. The modified strategy in Kondo reveals high-value, distance-independent entanglement mediated by the cloud, while in the dimer phase, entanglement is end-to-end and decays exponentially. The presentation also covers interacting clouds, impurity entanglement, and results emphasizing entanglement measures in capturing Kondo physics properties, generating oscillatory dynamics in the Kondo regime, and mediating long-range distance-independent entanglement through Kondo clouds.

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Entanglement in the Kondo Spin Chain

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  1. Entanglement in the Kondo Spin Chain Abolfazl Bayat1, Sougato Bose1, Pasquale Sodano2 1 University College London, London, UK. 2 University of Perugia, Perugia, Italy. Engineering of States and Devices: Theory and Experiments

  2. Contents of the Talk Quantum Information Condensed Matter 1. Kondo physics 2. Entanglement in the Kondo ground state 3. Generating a long range entanglement

  3. Gapped Systems Excited states Ground state The intrinsic length scale of the system impose an exponential decay

  4. Gapless Systems Continuum of excited states Ground state There is no length scale in the system so correlations decay algebraically

  5. Kondo Physics Despite the gapless nature of the Kondo system, correlations decay exponentially

  6. Kondo Spin Chain E. S. Sorensen et al., J. Stat. Mech., P08003 (2007)

  7. Entanglement as a Witness of the Cloud A B Impurity L

  8. Scaling B A Impurity L N-L-1 Kondo Phase: Dimer Phase:

  9. Scaling Properties of the Kondo regime Kondo Phase: Dimer Phase:

  10. Local Quench Quench

  11. Kondo versus Dimer

  12. Optimal Parameter

  13. Optimality and Distance independence Independent of length N, when cloud contains N-2 spins we generate a constant Entanglement

  14. Modified Strategy

  15. Entanglement in the Modified Strategy Kondo: High value distance independent entanglement mediated by the cloud. Dimer: Entanglement is just due to an end-end effect which decays exponentially.

  16. More fun with Kondo

  17. Entanglement Rotor Dispatching centre With interacting the clouds impurities get entangled

  18. Summary of Results • With using the entanglement measures, one can capture the properties of the Kondo physics. • A local quench generates an oscillatory dynamics in the Kondo regime. • Kondo cloud mediates long range distance independent • entanglement between individual ending. • References: • 1- Abolfazl Bayat, Pasquale Sodano, Sougato Bose, Physical Review B 81, 064429 (2010) • 2- Pasquale Sodano, Abolfazl Bayat,Sougato Bose, Physical Review B 81, 100412(R) (2010)

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