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

Contents of the Talk

Condensed Matter

Quantum Information

1. Kondo physics

2. Entanglement in the Kondo ground state

3. Generating a long range entanglement

Gapped Systems

Ground state

Excited states

||

:ji

jx

ix eSS

The intrinsic length scale of the system impose an exponential decay

Gapless Systems

0 : N Ground state

Continuum of excited states

|| jiSS jx

ix

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

Kondo Physics

Despite the gapless nature of the Kondo system, correlations decay exponentially

K

KK T

Kondo Spin Chain

2

2211312211 ..)..('i

iiii JJJJJH

(gapfull)Dimer :

(gapless) Kondo :2412.0

21

2

21

2

c

c

JJ

J

JJ

J

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

Entanglement as a Witness of the Cloud

A BImpurity

L

01 : SBSAK EEL

01 : SBSAK EEL

01 : SBSAK EEL

K

Scaling

),(),,(N

LNENLE

KK

),(),,(L

NLENLE

K

Kondo Phase:

Dimer Phase:

A BImpurity

L N-L-1

Scaling Properties of the Kondo regime

'/ JK e

4K

N

),(),,(N

LNENLE

KK

),,( NLE

Kondo Phase:

Dimer Phase:

K

Local Quench

iiiii

NNNN

JJ

JJJJJH

2211

22312112112

..

)....('

2

22113122111 ..)..('i

iiii JJJJJH

Quench

1)0( HGS

12)( HtiH GSet )(1 tN )(1 tE N

Kondo versus Dimer

Optimal Parameter

)'(JK

2

NK

2

NK 2NK

Optimality and Distance independence

Independent of length N, when cloud contains N-2 spins we generate a constant Entanglement

2)'( NJ optK

Modified Strategy

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.

More fun with Kondo

Entanglement Rotor

Dispatching centre

With interacting the clouds impurities get entangled

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)