Entanglement in the Kondo Spin Chain

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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
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Contents of the Talk
Quantum Information
Condensed Matter
1. Kondo physics
2. Entanglement in the Kondo ground state
3. Generating a long range entanglement
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Gapped Systems
Excited states
Ground state
The intrinsic length scale of the system impose
an exponential decay
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Gapless Systems
Continuum of excited states
Ground state
There is no length scale in the system so
correlations decay algebraically
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Kondo Physics
Despite the gapless nature of the Kondo system,
correlations decay exponentially
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Kondo Spin Chain
E. S. Sorensen et al., J. Stat. Mech., P08003
(2007)
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Entanglement as a Witness of the Cloud
A
B
Impurity

L
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Scaling
B
A
Impurity
L
N-L-1
Kondo Phase
Dimer Phase
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Scaling Properties of the Kondo regime

Kondo Phase
Dimer Phase
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Local Quench
Quench
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Kondo versus Dimer
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Optimal Parameter
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Optimality and Distance independence
Independent of length N, when cloud contains N-2
spins we generate a constant Entanglement
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Modified Strategy
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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.
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More fun with Kondo
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Entanglement Rotor
Dispatching centre
With interacting the clouds impurities get
entangled
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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)