dorsal/arxiv
View SchemaQuantum Entanglement in the Two Impurity Kondo Model
| Authors | Sam Young Cho, Ross H. McKenzie |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0509207 |
| URL | https://arxiv.org/abs/quant-ph/0509207 |
| DOI | 10.1103/PhysRevA.73.012109 |
Abstract
In order to quantify quantum entanglement in two impurity Kondo systems, we calculate the concurrence, negativity, and von Neumann entropy. The entanglement of the two Kondo impurities is shown to be determined by two competing many-body effects, the Kondo effect and the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, $I$. Due to the spin-rotational invariance of the ground state, the concurrence and negativity are uniquely determined by the spin-spin correlation between the impurities. It is found that there exists a critical minimum value of the antiferromagnetic correlation between the impurity spins which is necessary for entanglement of the two impurity spins. The critical value is discussed in relation with the unstable fixed point in the two impurity Kondo problem. Specifically, at the fixed point there is no entanglement between the impurity spins. Entanglement will only be created (and quantum information processing (QIP) be possible) if the RKKY interaction exchange energy, $I$, is at least several times larger than the Kondo temperature, $T_K$. Quantitative criteria for QIP are given in terms of the impurity spin-spin correlation.
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"abstract": "In order to quantify quantum entanglement in two impurity Kondo systems, we\ncalculate the concurrence, negativity, and von Neumann entropy. The\nentanglement of the two Kondo impurities is shown to be determined by two\ncompeting many-body effects, the Kondo effect and the\nRuderman-Kittel-Kasuya-Yosida (RKKY) interaction, $I$. Due to the\nspin-rotational invariance of the ground state, the concurrence and negativity\nare uniquely determined by the spin-spin correlation between the impurities. It\nis found that there exists a critical minimum value of the antiferromagnetic\ncorrelation between the impurity spins which is necessary for entanglement of\nthe two impurity spins. The critical value is discussed in relation with the\nunstable fixed point in the two impurity Kondo problem. Specifically, at the\nfixed point there is no entanglement between the impurity spins. Entanglement\nwill only be created (and quantum information processing (QIP) be possible) if\nthe RKKY interaction exchange energy, $I$, is at least several times larger\nthan the Kondo temperature, $T_K$. Quantitative criteria for QIP are given in\nterms of the impurity spin-spin correlation.",
"arxiv_id": "quant-ph/0509207",
"authors": [
"Sam Young Cho",
"Ross H. McKenzie"
],
"categories": [
"quant-ph",
"cond-mat.mes-hall"
],
"doi": "10.1103/PhysRevA.73.012109",
"title": "Quantum Entanglement in the Two Impurity Kondo Model",
"url": "https://arxiv.org/abs/quant-ph/0509207"
},
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