Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1112.1279 · Physical Review A

Global entanglement in XXZ chains

N. Canosa, R. Rossignoli

Published Feb 28, 2006• 38 citations
arXivHTMLPDF

Abstract

We examine the thermal entanglement of $XXZ$-type Heisenberg chains in the presence of a uniform magnetic field along the $z$ axes through the evaluation of the negativity associated with bipartitions of the whole system and subsystems. Limit temperatures for nonzero global negativities are shown to depend on the asymmetry $\ensuremath{\Delta}$, but not on the uniform field, and can be much higher than those limiting pairwise entanglement. It is also shown that global bipartite entanglement may exist for $T>0$ even for $\ensuremath{\Delta}\ensuremath{\geqslant}1$, i.e., when the system is fully aligned (and hence separable) at $T=0$, and that the bipartition leading to the highest limit temperature depends on $\ensuremath{\Delta}$.

DOI
10.1103/physreva.73.022347

Related papers

Global thermal entanglement in n -qubit systems

R. Rossignoli, N. Canosa

We examine the entanglement of thermal states of $n$ spins interacting through different types of $XY$ couplings in the presence of a uniform magnetic field, by evaluating the negativities of all possible bipartite partitions of the whole system and of subsystems. We consider both the case where every qubit interacts with all others and where just nearest neighbors interact in a one-dimensional chain. Limit temperatures for nonzero negativities are also evaluated and compared with the mean field critical temperature. It is shown that limit temperatures of global negativities are strictly independent of the magnetic field in all $XXZ$ models, in spite of the quantum transitions that these models may exhibit at zero temperature, while in anisotropic models they always increase for sufficiently large fields. Results also show that these temperatures are higher than those limiting pairwise entanglement.

arXiv:1312.7370•Physical Review A•Jul 26, 2005•34 citations

THERMAL ENTANGLEMENT IN SPIN SYSTEMS

N. Canosa, R. Rossignoli

We examine the entanglement of thermal states of n spins interacting through an XYZ type Heisenberg coupling in the presence of a uniform magnetic field, by evaluating the negativities of bipartite partitions of the whole system and subsystems. The corresponding limit temperatures for entanglement are also examined. Results indicate that limit temperatures for global entanglement depend on the type of partition and are higher than those limiting pairwise entanglement, and that their behavior with anisotropy and applied magnetic field may differ significantly from that of the corresponding mean field critical temperature.

International Journal of Modern Physics B•Dec 15, 2006•1 citation

Multipartite entanglement in the Heisenberg XX chain with impurity

Qin Meng, 中国人民解放军理工大学理学院,南京 211101

We studied the entanglements of the Heisenberg XX chain with impurity in the presence of a uniform magnetic field along the z axes by means of negativity. Through analyzing NL-A and N1-A, we show that the critical temperatures for nonzero negativities depend on the impurity parameter J1 and the magnetic field B. It is also shown that as qubit L increases, the entanglements increase when L is odd but decrease when L is even. And the entanglements of the even-qubit chains are larger than those of the odd-qubit chains. The condition is similar with L=3 for NL-A when qubit L is odd, but the entanglements increase with the increase of even qubit L.

Acta Physica Sinica•Jan 1, 2010•3 citations

The thermal entanglement in a spin-1 Heisenberg XXZ chain

Ni Hui-Ying, Jianxing Fang, Xiaoyan Zhou +1 more

In this paper, the entanglement in a spin-1 Heisenberg XXZ chain with uniform and nonuniform external magnetic field is investigated in the terms of the measure of entanglement called 'negativity'. The effects of the external magnetic field, the anisotropy parameter and the temperature on the negativity are discussed respectively. It can be seen that the entanglement in this spin chain for any temperature is symmetric with respect to zero magnetic field. We calculate the partially transposed density matrix and give qualitatively results at different temperatures. In order to show the results clearly, the behavior of negativity is presented for five different cases. It can be found that the temperature and the external magnetic field can effect the feature of the thermal entanglement significantly. In addition, under certain condition, the negativity may be enhanced under a nonuniform magnetic field.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Oct 26, 2007•0 citations

The effect of impurity on the thermal entanglement in three-qutrit spin-1 Heisenberg XXX chain

Qin Meng, Tian Dong-Ping, Tao Ying-Juan +1 more

We investigate the impurity entanglement of 3-qutrit XXX-type Heisenberg chains in the presence of a uniform magnetic field along z axis by means of negativity. The entanglement is calculated as a function of the coupling constants J, impurity parameter J1, magnetic fields B and temperature T. Through calculating the negativity between sites 1 and (2,3) N1-23 and sites 3 and (1,2) N12-3, we show that the critical temperature Tc above which the entanglement vanishes increases with the increase of J1. The existence of magnetic fields B can obviously reduce the entanglement, and it is found that the limiting temperature Tc depends on the impurity parameter J1 but not on the magnetic field.

Acta Physica Sinica•Jan 1, 2008•9 citations

Entanglement in a two-spin (1/2, 3/2) mixed-spin Heisenberg XXZ chain with an inhomogeneous external magnetic field

Ke-Tao Guo, M. M. Liang, Hong-Yu Xu +1 more

Using the concept of negativity, we investigate the thermal entanglement of a two-spin (1/2, 3/2) mixed-spin Heisenberg XXZ chain with an inhomogeneous external magnetic field. We obtain the analytical results of entanglement of this model. For the case of uniform magnetic field, we find that the critical temperature increases with the increase of the anisotropy parameter k , and for the same couplings, the critical temperature is higher than the results of the spin-1/2 XXZ chain and (1/2, 1) mixed-spin XXZ chain. Evidence of the quantum phase transition is found, and by adjusting the inhomogeneous magnetic parameter b , one is able to obtain more entanglement at higher temperature.

Journal of Physics A Mathematical and Theoretical•Nov 22, 2010•15 citations
We examine the thermal entanglement of XXZXXZXXZ-type Heisenberg chains in the presence of a uniform magnetic field along the zzz axes through the evaluation of the negativity associated with bipartitions of the whole system and subsystems. Limit temperatures for nonzero global negativities are shown to depend on the asymmetry \ensuremathΔ\ensuremath{\Delta}\ensuremathΔ, but not on the uniform field, and can be much higher than those limiting pairwise entanglement. It is also shown that global bipartite entanglement may exist for T>0T>0T>0 even for \ensuremathΔ\ensuremath⩾1\ensuremath{\Delta}\ensuremath{\geqslant}1\ensuremathΔ\ensuremath⩾1, i.e., when the system is fully aligned (and hence separable) at T=0T=0T=0, and that the bipartition leading to the highest limit temperature depends on \ensuremathΔ\ensuremath{\Delta}\ensuremathΔ.
We examine the entanglement of thermal states of nnn spins interacting through different types of XYXYXY couplings in the presence of a uniform magnetic field, by evaluating the negativities of all possible bipartite partitions of the whole system and of subsystems. We consider both the case where every qubit interacts with all others and where just nearest neighbors interact in a one-dimensional chain. Limit temperatures for nonzero negativities are also evaluated and compared with the mean field critical temperature. It is shown that limit temperatures of global negativities are strictly independent of the magnetic field in all XXZXXZXXZ models, in spite of the quantum transitions that these models may exhibit at zero temperature, while in anisotropic models they always increase for sufficiently large fields. Results also show that these temperatures are higher than those limiting pairwise entanglement.
We examine the entanglement of thermal states of n spins interacting through an XYZ type Heisenberg coupling in the presence of a uniform magnetic field, by evaluating the negativities of bipartite partitions of the whole system and subsystems. The corresponding limit temperatures for entanglement are also examined. Results indicate that limit temperatures for global entanglement depend on the type of partition and are higher than those limiting pairwise entanglement, and that their behavior with anisotropy and applied magnetic field may differ significantly from that of the corresponding mean field critical temperature.
We studied the entanglements of the Heisenberg XX chain with impurity in the presence of a uniform magnetic field along the z axes by means of negativity. Through analyzing NL-A and N1-A, we show that the critical temperatures for nonzero negativities depend on the impurity parameter J1 and the magnetic field B. It is also shown that as qubit L increases, the entanglements increase when L is odd but decrease when L is even. And the entanglements of the even-qubit chains are larger than those of the odd-qubit chains. The condition is similar with L=3 for NL-A when qubit L is odd, but the entanglements increase with the increase of even qubit L.
In this paper, the entanglement in a spin-1 Heisenberg XXZ chain with uniform and nonuniform external magnetic field is investigated in the terms of the measure of entanglement called 'negativity'. The effects of the external magnetic field, the anisotropy parameter and the temperature on the negativity are discussed respectively. It can be seen that the entanglement in this spin chain for any temperature is symmetric with respect to zero magnetic field. We calculate the partially transposed density matrix and give qualitatively results at different temperatures. In order to show the results clearly, the behavior of negativity is presented for five different cases. It can be found that the temperature and the external magnetic field can effect the feature of the thermal entanglement significantly. In addition, under certain condition, the negativity may be enhanced under a nonuniform magnetic field.
We investigate the impurity entanglement of 3-qutrit XXX-type Heisenberg chains in the presence of a uniform magnetic field along z axis by means of negativity. The entanglement is calculated as a function of the coupling constants J, impurity parameter J1, magnetic fields B and temperature T. Through calculating the negativity between sites 1 and (2,3) N1-23 and sites 3 and (1,2) N12-3, we show that the critical temperature Tc above which the entanglement vanishes increases with the increase of J1. The existence of magnetic fields B can obviously reduce the entanglement, and it is found that the limiting temperature Tc depends on the impurity parameter J1 but not on the magnetic field.
Using the concept of negativity, we investigate the thermal entanglement of a two-spin (1/2, 3/2) mixed-spin Heisenberg XXZ chain with an inhomogeneous external magnetic field. We obtain the analytical results of entanglement of this model. For the case of uniform magnetic field, we find that the critical temperature increases with the increase of the anisotropy parameter k , and for the same couplings, the critical temperature is higher than the results of the spin-1/2 XXZ chain and (1/2, 1) mixed-spin XXZ chain. Evidence of the quantum phase transition is found, and by adjusting the inhomogeneous magnetic parameter b , one is able to obtain more entanglement at higher temperature.