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, namely 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) will only 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.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, namely 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) will only 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.

arXiv:quant-ph/0509207Physical Review AJan 19, 200663 citations

TWO KONDO IMPURITY PROBLEM: RELEVANCE TO HEAVY FERMIONS

Barbara Jones, C. M. Varma

Elsevier eBooksJan 1, 19871 citation

Solution of the Spin-1/2 Kondo Hamiltonian

Kenneth Geddes Wilson

Elsevier eBooksJan 1, 19733 citations

Exactly solvable Kondo problem in the open $t-J$ chainsExactly solvable Kondo problem in the open $t-J$ chains

Jianhui Dai, Yupeng Wang

We study the problem of a boundary magnetic impurity coupled with the solvable $t-J$ chains. Our model provides a good start point to understand the Kondo problem in a Luttinger liquid as well as in a strongly correlated host. The Kondo coupling constant $J$ can take arbitrary values, which allows us to study the ferromagnetic and antiferromagnetic Kondo problems simultaneously. It is shown that both the Kondo coupling and the scalar potential effectively reconcile the spin dynamics at low temperatures. Generally, the impurity spin is split into two ghost spins via coupling effect. The residual entropy, which can be exactly derived for the present model, is strongly interaction-dependent. This hints the local spin configuration is very complicated and very different from that in the conventional Kondo problem. An unscreening phenomenon in the antiferromagnetic regime is found, which reveals the impurity potential plays an important role for the Kondo problem in a strongly correlated host. The low temperature specific heat is calculated in the framework of local Landau-Luttinger liquid theory.We study the problem of a boundary magnetic impurity coupled with the solvable $t-J$ chains. Our model provides a good start point to understand the Kondo problem in a Luttinger liquid as well as in a strongly correlated host. The Kondo coupling constant $J$ can take arbitrary values, which allows us to study the ferromagnetic and antiferromagnetic Kondo problems simultaneously. It is shown that both the Kondo coupling and the scalar potential effectively reconcile the spin dynamics at low temperatures. Generally, the impurity spin is split into two ghost spins via coupling effect. The residual entropy, which can be exactly derived for the present model, is strongly interaction-dependent. This hints the local spin configuration is very complicated and very different from that in the conventional Kondo problem. An unscreening phenomenon in the antiferromagnetic regime is found, which reveals the impurity potential plays an important role for the Kondo problem in a strongly correlated host. The low temperature specific heat is calculated in the framework of local Landau-Luttinger liquid theory.

arXiv:cond-mat/9809008Sep 1, 19980 citations

Coherence in the Two Kondo Impurity Problem

Lijun Zhu, Chandra Mohan Varma

We show through a perturbative and an exact calculation using Wilson's renormalization methods that in the problem of two interacting Kondo impurities, on-site potential scattering generates a quantum-tunneling between the two impurities through a marginally relevant operator. The magnitude of this tunneling $V_{12}$ depends on the spin-correlation between the two impurities. For exchange interactions between the moments comparable to the Kondo energy $T_K$ , $V_{12}$ is typically much larger than $T_K$ . This implies that the heavy-fermion mass in this interesting range is determined by $V_{12}$ rather than $T_K$ . The importance of these results for experiments in coupled Kondo dots is also pointed out.We show through a perturbative and an exact calculation using Wilson's renormalization methods that in the problem of two interacting Kondo impurities, on-site potential scattering generates a quantum-tunneling between the two impurities through a marginally relevant operator. The magnitude of this tunneling $V_{12}$ depends on the spin-correlation between the two impurities. For exchange interactions between the moments comparable to the Kondo energy $T_K$, $V_{12}$ is typically much larger than $T_K$. This implies that the heavy-fermion mass in this interesting range is determined by $V_{12}$ rather than $T_K$. The importance of these results for experiments in coupled Kondo dots is also pointed out.

arXiv:cond-mat/0607426Jul 17, 20061 citation

Numerical Renormalization Group Approach to the Two-Impurity Kondo Hamiltonian

Barbara Jones

Jun 1, 19880 citations

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) will only 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.

Exactly solvable Kondo problem in the open

t-J

chains

We study the problem of a boundary magnetic impurity coupled with the solvable

t-J

chains. Our model provides a good start point to understand the Kondo problem in a Luttinger liquid as well as in a strongly correlated host. The Kondo coupling constant

J

can take arbitrary values, which allows us to study the ferromagnetic and antiferromagnetic Kondo problems simultaneously. It is shown that both the Kondo coupling and the scalar potential effectively reconcile the spin dynamics at low temperatures. Generally, the impurity spin is split into two ghost spins via coupling effect. The residual entropy, which can be exactly derived for the present model, is strongly interaction-dependent. This hints the local spin configuration is very complicated and very different from that in the conventional Kondo problem. An unscreening phenomenon in the antiferromagnetic regime is found, which reveals the impurity potential plays an important role for the Kondo problem in a strongly correlated host. The low temperature specific heat is calculated in the framework of local Landau-Luttinger liquid theory.

V_{12}

depends on the spin-correlation between the two impurities. For exchange interactions between the moments comparable to the Kondo energy

T_K

V_{12}

is typically much larger than

T_K

. This implies that the heavy-fermion mass in this interesting range is determined by

V_{12}

rather than

T_K

. The importance of these results for experiments in coupled Kondo dots is also pointed out.