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Macroscopic thermal entanglement in a spin chain caused by the magnetic field: Inhomogeneity effect
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10.1063/1.3691529
/content/aip/journal/ltp/38/3/10.1063/1.3691529
http://aip.metastore.ingenta.com/content/aip/journal/ltp/38/3/10.1063/1.3691529
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Localization length ξ1 as the function of the relative strength of the impurity-host coupling I = J′/J and the relative strength of the magnetic field, which affects the spin of the impurity x = (γ′ − γ)H/J. One can see that for some values of the impurity-host strength and the field the correlation length can be of order of 500 sites of the chain.

Image of FIG. 2.
FIG. 2.

The ground-state tangles τav (dotted line), τ0 (solid line), and τ1 (dashed line) as the function of the applied magnetic field H (we use units in which Planck’s and Boltzmann’s constants, gyromagnetic ratio γ and the exchange integral J in the chain are equal to 1 for I = 2.2 and α = 1.2). τ0 and τ1 manifest jumps at H 0 = I 2 J/2γ(α(I 2 − α))1/2 which take place in the region of the parameters for the impurity (Ref. 20) I 2 > 2γ′/(1 + α), as the contribution of the local level. The average tangle shows no low-temperature jump at H 0 comparing to the ones for the impurity site and near the impurity; instead τav manifests the kink (due to the second order quantum phase transition) at the critical value Hs  = J/γ, characteristic for the homogeneous system.

Image of FIG. 3.
FIG. 3.

The ground-state tangles τ4 (dashed line), and τ5 (solid line) as the function of the applied magnetic field H (parameters are the same as in Fig.2). We can see the jump at H 0, however the value of tangles are much smaller than in the vicinity of the inhomogeneity.

Image of FIG. 4.
FIG. 4.

The average concurrence C av as the function of temperature T and the applied magnetic field H for J = 1.

Image of FIG. 5.
FIG. 5.

The concurrence C 01 at the impurity site as the function of temperature T and the applied magnetic field H. Parameters are the same as in Fig.2. The concurrence becomes smaller with the growth of the field.

Image of FIG. 6.
FIG. 6.

The concurrence C 45 in a short distance from the impurity as the function of temperature T and the applied magnetic field H. Parameters are the same as in Fig. 2. Notice much smaller scale for C 45 comparing to C 01. The concurrence is zero at H = 0 and becomes nonzero for large enough H.

Image of FIG. 7.
FIG. 7.

The concurrence C 01 at the impurity qubit as the function of temperature T and the parameter of the inhomogeneity I at zero field H = 0.

Image of FIG. 8.
FIG. 8.

The concurrence C 12 for the nearest to the impurity qubits as the function of temperature T and the parameter of the inhomogeneity I at zero field H = 0.

Image of FIG. 9.
FIG. 9.

The concurrence C 01 at the impurity site as the function of temperature T at the applied magnetic field H = 0.5J/γ. Parameters are the same as in Fig. 2.

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/content/aip/journal/ltp/38/3/10.1063/1.3691529
2012-03-27
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Macroscopic thermal entanglement in a spin chain caused by the magnetic field: Inhomogeneity effect
http://aip.metastore.ingenta.com/content/aip/journal/ltp/38/3/10.1063/1.3691529
10.1063/1.3691529
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