entanglement in the kondo spin chain abolfazl bayat 1, sougato bose 1, pasquale sodano 2 1...
TRANSCRIPT
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)
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
Optimality and Distance independence
Independent of length N, when cloud contains N-2 spins we generate a constant Entanglement
2)'( NJ optK
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.
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)