Kondo physics from a quantum information perspective
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Kondo Physics from a Quantum Information Perspective. Pasquale Sodano International Institute of Physics, Natal, Brazil. Sougato Bose UCL (UK). Henrik Johannesson Gothenburg (Sweden). Abolfazl Bayat UCL (UK). References. An order parameter for impurity systems at quantum criticality

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Kondo physics from a quantum information perspective

Kondo Physics from a Quantum Information Perspective

Pasquale Sodano

International Institute of Physics, Natal, Brazil


Kondo physics from a quantum information perspective

Sougato Bose

UCL (UK)

Henrik Johannesson

Gothenburg (Sweden)

AbolfazlBayat

UCL (UK)


References

References

  • An order parameter for impurity systems at quantum criticality

  • A. Bayat, H. Johannesson, S. Bose, P. Sodano

  • To appear in Nature Communication.

  • Entanglement probe of two-impurity Kondo physics in a spin chain

  • A. Bayat, S. Bose, P. Sodano, H. Johannesson, Phys. Rev. Lett. 109, 066403 (2012)

  • Entanglement Routers Using Macroscopic Singlets

  • A. Bayat, S. Bose, P. Sodano, Phys. Rev. Lett. 105, 187204 (2010)

  • Negativity as the Entanglement Measure to Probe the Kondo Regime in the

  • Spin-Chain Kondo Model

  • A. Bayat, P. Sodano, S. Bose, Phys. Rev. B 81, 064429 (2010)

  • Kondo Cloud Mediated Long Range Entanglement After Local

  • Quench in a Spin Chain

  • P. Sodano, A. Bayat, S. Bose

  • Phys. Rev. B 81, 100412(R) (2010)


Contents of the talk

Contents of the Talk

Negativity as an Entanglement Measure

Single Kondo Impurity Model

Application: Quantum Router

Two Impurity Kondo model: Entanglement

Two Impurity Kondo model: Entanglement Spectrum


Entanglement of mixed states

Entanglement of Mixed States

Separable states:

Entangled states:

How to quantify entanglement for a general mixed state?

There is not a unique entanglement measure


Negativity

Negativity

Separable:

Valid density matrix

Entangled:

Negativity:


Gapped systems

Gapped Systems

Excited states

Ground state

The intrinsic length scale of the system impose an exponential decay


Gapless systems

Gapless Systems

Continuum of excited states

Ground state

There is no length scale in the system so correlations decay algebraically


Kondo physics

Kondo Physics

Despite the gapless nature of the Kondo system, we have a length scale in the model


Realization of kondo effect

Realization of Kondo Effect

Semiconductor quantum dots

D. G. Gordon et al. Nature 391, 156 (1998).

S.M. Cronenwett, Science 281, 540 (1998).

Carbon nanotubes

J. Nygard, et al. Nature 408, 342 (2000).

M. Buitelaar, Phys. Rev. Lett. 88, 156801 (2002).

Individual molecules

J. Park, et al. Nature 417, 722 (2002).

W. Liang, et al, Nature 417, 725–729 (2002).


Kondo spin chain

Kondo Spin Chain

E. S. Sorensen et al., J. Stat. Mech., P08003 (2007)


Entanglement as a witness of the cloud

Entanglement as a Witness of the Cloud

A

B

Impurity

L


Entanglement versus length

Entanglement versus Length

Entanglement decays exponentially with length


Scaling

Scaling

B

A

Impurity

L

N-L-1

Kondo Regime:

Dimer Regime:


Scaling of the kondo cloud

Scaling of the Kondo Cloud

Kondo Phase:

Dimer Phase:


Application quantum router

Application: Quantum Router

Converting useless entanglement into useful

one through quantum quench


Simple example

Simple Example


Extended singlet

Extended Singlet

With tuning J’ we can generate a proper cloud which

extends till the end of the chain


Quench dynamics

Quench Dynamics


Attainable entanglement

Attainable Entanglement

1- Entanglement dynamics is very long lived and oscillatory

2- maximal entanglement attains a constant values for large chains

3- The optimal time which entanglement peaks is linear


Distance independence

Distance Independence

For simplicity take a symmetric composite:


Optimal quench

Optimal Quench


Optimal parameter

Optimal Parameter


Non kondo singlets dimer regime

Non-Kondo Singlets (Dimer Regime)

Clouds are absent

K: Kondo (J2=0) D: Dimer (J2=0.42)


Asymmetric chains

Asymmetric Chains


Entanglement in asymmetric chains

Entanglement in Asymmetric Chains

Symmetric geometry gives the best output


Entanglement router

Entanglement Router


Two impurity kondo model

Two Impurity Kondo Model


Two impurity kondo model1

Two Impurity Kondo Model

RKKY interaction


Impurities

Impurities

Entanglement


Entanglement of impurities

Entanglement of Impurities

Entanglement can be used as the order parameter

for differentiating phases


Scaling at the phase transition

Scaling at the Phase Transition

The critical RKKY coupling scales just as Kondo temperature does


Entropy of impurities

Entropy of Impurities

Triplet

Identity

Singlet


Impurity block entanglement

Impurity-Block Entanglement


B lock block entanglement

Block-Block Entanglement


2 nd order phase transition

2nd Order Phase Transition


Kondo physics from a quantum information perspective

Order Parameter for Two Impurity Kondo Model


Order parameter

Order Parameter

  • Order parameter is:

    • 1- Observable

    • 2- Is zero in one phase and non-zero in the other

    • 3- Scales at criticality

  • Landau-Ginzburg paradigm:

    • 4- Order parameter is local

    • 5- Order parameter is associated with a symmetry breaking


Entanglement spectrum

Entanglement Spectrum

Entanglement spectrum:


Entanglement spectrum1

Entanglement Spectrum

NA=NB=400

J’=0.4

NA=600, NB=200

J’=0.4


Schmidt gap

Schmidt Gap

Schmidt gap:


Thermodynamic behaviour

Thermodynamic Behaviour

J’=0.4

J’=0.5

In the thermodynamic limit Schmidt gap takes

zero in the RKKY regime


Diverging derivative

Diverging Derivative

In the thermodynamic limit the first derivative of

Schmidt gap diverges


Diverging kondo length

Diverging Kondo Length


Finite size scaling

Finite Size Scaling


Schmidt gap as an observable

Schmidt Gap as an Observable


Summary

Summary

Negativity is enough to determine the Kondo length and the

scaling of the Kondo impurity problems.

By tuning the Kondo cloud one can route distance independent

entanglement between multiple users via a single bond quench.

Negativity also captures the quantum phase transition in two

impurity Kondo model.

Schmidt gap, as an observable, shows scaling with the right

exponents at the critical point of the two Impurity Kondo model.


References1

References

  • An order parameter for impurity systems at quantum criticality

  • A. Bayat, H. Johannesson, S. Bose, P. Sodano

  • To appear in Nature Communication.

  • Entanglement probe of two-impurity Kondo physics in a spin chain

  • A. Bayat, S. Bose, P. Sodano, H. Johannesson, Phys. Rev. Lett. 109, 066403 (2012)

  • Entanglement Routers Using Macroscopic Singlets

  • A. Bayat, S. Bose, P. Sodano, Phys. Rev. Lett. 105, 187204 (2010)

  • Negativity as the Entanglement Measure to Probe the Kondo Regime in the

  • Spin-Chain Kondo Model

  • A. Bayat, P. Sodano, S. Bose, Phys. Rev. B 81, 064429 (2010)

  • Kondo Cloud Mediated Long Range Entanglement After Local

  • Quench in a Spin Chain

  • P. Sodano, A. Bayat, S. Bose

  • Phys. Rev. B 81, 100412(R) (2010)


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