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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International Institute of Physics, Natal, Brazil
Negativity as an Entanglement Measure
Single Kondo Impurity Model
Application: Quantum Router
Two Impurity Kondo model: Entanglement
Two Impurity Kondo model: Entanglement Spectrum
How to quantify entanglement for a general mixed state?
There is not a unique entanglement measure
Valid density matrix
The intrinsic length scale of the system impose an exponential decay
Continuum of excited states
There is no length scale in the system so correlations decay algebraically
Despite the gapless nature of the Kondo system, we have a length scale in the model
Semiconductor quantum dots
D. G. Gordon et al. Nature 391, 156 (1998).
S.M. Cronenwett, Science 281, 540 (1998).
J. Nygard, et al. Nature 408, 342 (2000).
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J. Park, et al. Nature 417, 722 (2002).
W. Liang, et al, Nature 417, 725–729 (2002).
E. S. Sorensen et al., J. Stat. Mech., P08003 (2007)
Entanglement decays exponentially with length
Converting useless entanglement into useful
one through quantum quench
With tuning J’ we can generate a proper cloud which
extends till the end of the chain
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
For simplicity take a symmetric composite:
Clouds are absent
K: Kondo (J2=0) D: Dimer (J2=0.42)
Symmetric geometry gives the best output
Entanglement can be used as the order parameter
for differentiating phases
The critical RKKY coupling scales just as Kondo temperature does
In the thermodynamic limit Schmidt gap takes
zero in the RKKY regime
In the thermodynamic limit the first derivative of
Schmidt gap diverges
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.