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:1210.0596 · Physical Review A

Thermal entanglement in an exactly solvable Ising-XXZdiamond chain structure

Onofre Rojas, Moisés Rojas, N.S. Ananikian, S. M. de Souza

Published Oct 22, 2012• 83 citations
arXivHTMLPDF

Abstract

Most quantum entanglement investigations are focused on two qubits or some finite (small) chain structure, since the infinite chain structure is a considerably cumbersome task. Therefore, the quantum entanglement properties involving an infinite chain structure is quite important, not only because the mathematical calculation is cumbersome but also because real materials are well represented by an infinite chain. Thus, in this paper we consider an entangled diamond chain with Ising and anisotropic Heisenberg (Ising-XXZ) coupling. Two interstitial particles are coupled through Heisenberg coupling or simply two-qubit Heisenberg, which could be responsible for the emergence of entanglement. These two-qubit Heisenberg operators are interacted with two nodal Ising spins. An infinite diamond chain is organized by interstitial-interstitial and nodal-interstitial (dimer-monomer) site couplings. We are able to get the thermal average of the two-qubit operator, called the reduced two-qubit density operator. Since these density operators are spatially separated, we could obtain the concurrence (entanglement) directly in the thermodynamic limit. The thermal entanglement (concurrence) is constructed for different values of the anisotropic Heisenberg parameter, magnetic field, and temperature. We also observed the threshold temperature via the parameter of anisotropy, Heisenberg and Ising interaction, external magnetic field, and temperature.

DOI
10.1103/physreva.86.042330

Related papers

Pairwise thermal entanglement in the Ising-XYZ diamond chain structure in an external magnetic field

Jordana Torrico, M. Rojas, S. M. de Souza +2 more

Quantum entanglement is one of the most fascinating types of correlation that can be shared only among quantum systems. The Heisenberg chain is one of the simplest quantum chains which exhibits a reach entanglement feature, due to the Heisenberg interaction is quantum coupling in the spin system. The two particles were coupled trough XYZ coupling or simply called as two-qubit XYZ spin, which are the responsible for the emergence of thermal entanglement. These two-qubit operators are bonded to two nodal Ising spins, and this process is repeated infinitely resulting in a diamond chain structure. We will discuss two-qubit thermal entanglement effect on Ising-XYZ diamond chain structure. The concurrence could be obtained straightforwardly in terms of two-qubit density operator elements, using this result, we study the thermal entanglement, as well as the threshold temperature where entangled state vanishes. The present model displays a quite unusual concurrence behavior, such as, the boundary of two entangled regions becomes a disentangled region, this is intrinsically related to the XY-anisotropy in the Heisenberg coupling. Despite a similar property had been found for only two-qubit, here we show in the case of a diamond chain structure, which reasonably represents real materials.

arXiv:1409.6935•Europhysics Letters (EPL)•Dec 1, 2014•62 citations

Thermal entanglement of a spin-1/2 Ising–Heisenberg model on a symmetrical diamond chain

N.S. Ananikian, L N Ananikyan, Levon Chakhmakhchyan +1 more

The entanglement quantum properties of a spin-1/2 Ising-Heisenberg model on a symmetrical diamond chain were analyzed. Due to the separable nature of the Ising-type exchange interactions between neighboring Heisenberg dimers, calculation of the entanglement can be performed exactly for each individual dimer. Pairwise thermal entanglement was studied in terms of the isotropic Ising-Heisenberg model and analytical expressions for the concurrence (as a measure of bipartite entanglement) were obtained. The effects of external magnetic field H and next-nearest neighbor interaction J(m) between nodal Ising sites were considered. The ground state structure and entanglement properties of the system were studied in a wide range of coupling constant values. Various regimes with different values of ground state entanglement were revealed, depending on the relation between competing interaction strengths. Finally, some novel effects, such as the two-peak behavior of concurrence versus temperature and coexistence of phases with different values of magnetic entanglement, were observed.

arXiv:1110.6406•Journal of Physics Condensed Matter•May 25, 2012•64 citations

Thermal entanglement of the spin-1 Ising–Heisenberg diamond chain with biquadratic interaction

Yidan Zheng, Zhu Mao, Bin Zhou

We investigate the thermal entanglement of the spin-1 Ising–Heisenberg diamond chain, which can be regarded as a theoretical model for the homometallic molecular ferrimagnet [ Ni 3 ( C 4 H 2 O 4 ) 2 − ( μ 3 − OH ) 2 ( H 2 O ) 4 ] n ⋅ ( 2 H 2 O ) n . Two cases, i.e., the isotropic Heisenberg (Ising–XXX) coupling model and anisotropic Heisenberg (Ising–XXZ) coupling model, are discussed respectively. The negativity is chosen as the measurement of the thermal entanglement. By means of the transfer-matrix approach, we focus on the effects of biquadratic interaction parameters on the negativity of the infinite spin-1 Ising–Heisenberg diamond chain. In the Ising–XXX coupling model, it is shown that for the case with ferromagnetic coupling the thermal entanglement can be induced by the biquadratic interaction, but the external magnetic field will suppress the occurrence of the entanglement induced by the biquadratic interaction. In the Ising–XXZ coupling model, for the case with antiferromagnetic coupling, due to the biquadratic interaction the effect of the anisotropy parameter on the entanglement will be suppressed at near-zero temperature. Moreover, the biquadratic interaction makes the threshold temperature increase. The effects of the external magnetic field on the thermal entanglement are also discussed, and it is observed that the entanglement revival phenomena exist in both models considered.

Chinese Physics B•Jun 1, 2017•3 citations

Thermal entanglement of the spin-1/2 diamond chain

Levon Chakhmakhchyan, N.S. Ananikian, L. Ananikyan +1 more

The entanglement thermal (equilibrium) properties in spin-1/2 Ising-Heisenberg model on an ideal diamond chain is analyzed. Due to the classical character of Ising-type exchange interactions between two neighboring antiferromagnetic Heisenberg dimers, the calculation of quantum entanglement (by tracing out Ising spins) can be performed for each of the dimers separately. The concurrence, as a measure of entanglement is obtained and different regimes depending on the values of exchange interactions are revealed. The effects of the magnetic field are incorporated and critical temperatures corresponding to the vanishing or arising of entanglement are considered.

Journal of Physics Conference Series•Feb 8, 2012•13 citations

Quantum entanglement in a quasi-phase region for a spin-1/2 Ising-XYZ diamond chain

I. M. Carvalho, Jordana Torrico, S. M. de Souza +2 more

We investigate a spin-1/2 Ising-XYZ diamond chain with Ising-like interaction between nodal and interstitial sites and Heisenberg-like interaction between interstitial sites, subjected to an external magnetic field applied along the $z$-direction. This model presents exact analytical solution and can be solved using the transfer matrix technique. Here, we study the entropy and quantum entanglement in the quasi-phase region, which can be quantified through concurrence. For the chosen parameters, the system presents three regions with different spin orientation at the finite temperature, which we call quasi-phase ferrimagnetic ($qFI$) and two types of quasi-phase ferromagnetic Ising and modulated ferromagnetic Heisenberg ($qMF_0$) and ($qMF_2$). We show that the quantum entanglement remains almost constant in $qMF_0$ until considerable temperature values. In addition, we verify that the quantum entanglement is null in the pseudo-transition between the $qFI$ e $qMF_0$, but in the interface between $qMF_0$ and $qMF_2$ is entangled. We observe an abrupt increase in the entropy curves in the pseudo-critical temperature. We also observe when the temperature is lower than the pseudo-critical temperature the entropy remains almost constant at zero and the quantum entanglement in this same region remains almost constant.

•Dec 15, 2017•0 citations

Thermal entanglement of the Ising–Heisenberg diamond chain with Dzyaloshinskii–Moriya interaction

Jie Qiao, Bin Zhou

We investigate the thermal entanglement in a spin-1/2 Ising–Heisenberg diamond chain, in which the vertical Heisenberg spin dimers alternate with single Ising spins. Due to the fact that the Dzyaloshinskii–Moriya (DM) interaction contributes to unusual and interesting magnetic properties in actual materials, and moreover it plays a significant role in the degree of the entanglement of the Heisenberg quantum spin systems, we focus on the effects of different DM interactions, including D z and D x , on the thermal entanglement of the Heisenberg spin dimer. The concurrence, as a measure of spin dimer entanglement, is calculated for different values of exchange interactions, DM interaction, external magnetic field, and temperature. It is found that the critical temperature and the critical magnetic field corresponding to the vanishing of entanglement increase with DM interaction, and the entanglement revival region gets larger by increasing DM interaction, thus DM interaction favors the formation of the thermal entanglement. It is observed that different DM interaction parameters ( D z and D x ) have remarkably different influences on the entanglement. Different from the case D z , there is the non-monotonic variation of the concurrence with temperature in the case D x , and additionally the DM interaction D x can induce the entanglement near zero temperature in the case that the antiferromagnetic Ising-type interaction constant is larger than the antiferromagnetic Heisenberg interaction constant. It is also shown that for the same value of DM interaction the critical magnetic field of the case D x is larger than that of the case D z .

Chinese Physics B•Nov 1, 2015•7 citations
Most quantum entanglement investigations are focused on two qubits or some finite (small) chain structure, since the infinite chain structure is a considerably cumbersome task. Therefore, the quantum entanglement properties involving an infinite chain structure is quite important, not only because the mathematical calculation is cumbersome but also because real materials are well represented by an infinite chain. Thus, in this paper we consider an entangled diamond chain with Ising and anisotropic Heisenberg (Ising-XXZ) coupling. Two interstitial particles are coupled through Heisenberg coupling or simply two-qubit Heisenberg, which could be responsible for the emergence of entanglement. These two-qubit Heisenberg operators are interacted with two nodal Ising spins. An infinite diamond chain is organized by interstitial-interstitial and nodal-interstitial (dimer-monomer) site couplings. We are able to get the thermal average of the two-qubit operator, called the reduced two-qubit density operator. Since these density operators are spatially separated, we could obtain the concurrence (entanglement) directly in the thermodynamic limit. The thermal entanglement (concurrence) is constructed for different values of the anisotropic Heisenberg parameter, magnetic field, and temperature. We also observed the threshold temperature via the parameter of anisotropy, Heisenberg and Ising interaction, external magnetic field, and temperature.
Quantum entanglement is one of the most fascinating types of correlation that can be shared only among quantum systems. The Heisenberg chain is one of the simplest quantum chains which exhibits a reach entanglement feature, due to the Heisenberg interaction is quantum coupling in the spin system. The two particles were coupled trough XYZ coupling or simply called as two-qubit XYZ spin, which are the responsible for the emergence of thermal entanglement. These two-qubit operators are bonded to two nodal Ising spins, and this process is repeated infinitely resulting in a diamond chain structure. We will discuss two-qubit thermal entanglement effect on Ising-XYZ diamond chain structure. The concurrence could be obtained straightforwardly in terms of two-qubit density operator elements, using this result, we study the thermal entanglement, as well as the threshold temperature where entangled state vanishes. The present model displays a quite unusual concurrence behavior, such as, the boundary of two entangled regions becomes a disentangled region, this is intrinsically related to the XY-anisotropy in the Heisenberg coupling. Despite a similar property had been found for only two-qubit, here we show in the case of a diamond chain structure, which reasonably represents real materials.
The entanglement quantum properties of a spin-1/2 Ising-Heisenberg model on a symmetrical diamond chain were analyzed. Due to the separable nature of the Ising-type exchange interactions between neighboring Heisenberg dimers, calculation of the entanglement can be performed exactly for each individual dimer. Pairwise thermal entanglement was studied in terms of the isotropic Ising-Heisenberg model and analytical expressions for the concurrence (as a measure of bipartite entanglement) were obtained. The effects of external magnetic field H and next-nearest neighbor interaction J(m) between nodal Ising sites were considered. The ground state structure and entanglement properties of the system were studied in a wide range of coupling constant values. Various regimes with different values of ground state entanglement were revealed, depending on the relation between competing interaction strengths. Finally, some novel effects, such as the two-peak behavior of concurrence versus temperature and coexistence of phases with different values of magnetic entanglement, were observed.
We investigate the thermal entanglement of the spin-1 Ising–Heisenberg diamond chain, which can be regarded as a theoretical model for the homometallic molecular ferrimagnet [ Ni 3 ( C 4 H 2 O 4 ) 2 − ( μ 3 − OH ) 2 ( H 2 O ) 4 ] n ⋅ ( 2 H 2 O ) n . Two cases, i.e., the isotropic Heisenberg (Ising–XXX) coupling model and anisotropic Heisenberg (Ising–XXZ) coupling model, are discussed respectively. The negativity is chosen as the measurement of the thermal entanglement. By means of the transfer-matrix approach, we focus on the effects of biquadratic interaction parameters on the negativity of the infinite spin-1 Ising–Heisenberg diamond chain. In the Ising–XXX coupling model, it is shown that for the case with ferromagnetic coupling the thermal entanglement can be induced by the biquadratic interaction, but the external magnetic field will suppress the occurrence of the entanglement induced by the biquadratic interaction. In the Ising–XXZ coupling model, for the case with antiferromagnetic coupling, due to the biquadratic interaction the effect of the anisotropy parameter on the entanglement will be suppressed at near-zero temperature. Moreover, the biquadratic interaction makes the threshold temperature increase. The effects of the external magnetic field on the thermal entanglement are also discussed, and it is observed that the entanglement revival phenomena exist in both models considered.
The entanglement thermal (equilibrium) properties in spin-1/2 Ising-Heisenberg model on an ideal diamond chain is analyzed. Due to the classical character of Ising-type exchange interactions between two neighboring antiferromagnetic Heisenberg dimers, the calculation of quantum entanglement (by tracing out Ising spins) can be performed for each of the dimers separately. The concurrence, as a measure of entanglement is obtained and different regimes depending on the values of exchange interactions are revealed. The effects of the magnetic field are incorporated and critical temperatures corresponding to the vanishing or arising of entanglement are considered.
We investigate a spin-1/2 Ising-XYZ diamond chain with Ising-like interaction between nodal and interstitial sites and Heisenberg-like interaction between interstitial sites, subjected to an external magnetic field applied along the zzz-direction. This model presents exact analytical solution and can be solved using the transfer matrix technique. Here, we study the entropy and quantum entanglement in the quasi-phase region, which can be quantified through concurrence. For the chosen parameters, the system presents three regions with different spin orientation at the finite temperature, which we call quasi-phase ferrimagnetic (qFIqFIqFI) and two types of quasi-phase ferromagnetic Ising and modulated ferromagnetic Heisenberg (qMF0qMF_0qMF0​) and (qMF2qMF_2qMF2​). We show that the quantum entanglement remains almost constant in qMF0qMF_0qMF0​ until considerable temperature values. In addition, we verify that the quantum entanglement is null in the pseudo-transition between the qFIqFIqFI e qMF0qMF_0qMF0​, but in the interface between qMF0qMF_0qMF0​ and qMF2qMF_2qMF2​ is entangled. We observe an abrupt increase in the entropy curves in the pseudo-critical temperature. We also observe when the temperature is lower than the pseudo-critical temperature the entropy remains almost constant at zero and the quantum entanglement in this same region remains almost constant.
We investigate the thermal entanglement in a spin-1/2 Ising–Heisenberg diamond chain, in which the vertical Heisenberg spin dimers alternate with single Ising spins. Due to the fact that the Dzyaloshinskii–Moriya (DM) interaction contributes to unusual and interesting magnetic properties in actual materials, and moreover it plays a significant role in the degree of the entanglement of the Heisenberg quantum spin systems, we focus on the effects of different DM interactions, including D z and D x , on the thermal entanglement of the Heisenberg spin dimer. The concurrence, as a measure of spin dimer entanglement, is calculated for different values of exchange interactions, DM interaction, external magnetic field, and temperature. It is found that the critical temperature and the critical magnetic field corresponding to the vanishing of entanglement increase with DM interaction, and the entanglement revival region gets larger by increasing DM interaction, thus DM interaction favors the formation of the thermal entanglement. It is observed that different DM interaction parameters ( D z and D x ) have remarkably different influences on the entanglement. Different from the case D z , there is the non-monotonic variation of the concurrence with temperature in the case D x , and additionally the DM interaction D x can induce the entanglement near zero temperature in the case that the antiferromagnetic Ising-type interaction constant is larger than the antiferromagnetic Heisenberg interaction constant. It is also shown that for the same value of DM interaction the critical magnetic field of the case D x is larger than that of the case D z .