The nearest-neighbor spins in the one-dimensional spin-1/2 $XX$ model with the added Dzyaloshinskii-Moriya (DM) interaction are entangled at zero temperature. In the presence of a transverse magnetic field (TF) they remain entangled up to a quantum critical field, ${h}_{c}$ . Using the fermionization technique, we have studied the mutual effect of the DM interaction and a TF on the thermal entanglement (TE) in this model. The critical temperature where the entanglement disappears is specified. It is found that the TE in the finite-temperature neighborhood of the quantum critical field shows a scaling behavior with the critical exponent equal to the critical gap exponent. We also argue that thermodynamical properties like the specific heat and the magnetocaloric effect (instead of the usual internal energy and the magnetization) can detect the mentioned quantum entanglement in solid systems. In addition, we suggest a tactic to find all critical temperatures, which is based on the derivative of the entanglement witness with respect to the temperature.The nearest-neighbor spins in the one-dimensional spin-1/2 $XX$ model with the added Dzyaloshinskii-Moriya (DM) interaction are entangled at zero temperature. In the presence of a transverse magnetic field (TF) they remain entangled up to a quantum critical field, ${h}_{c}$. Using the fermionization technique, we have studied the mutual effect of the DM interaction and a TF on the thermal entanglement (TE) in this model. The critical temperature where the entanglement disappears is specified. It is found that the TE in the finite-temperature neighborhood of the quantum critical field shows a scaling behavior with the critical exponent equal to the critical gap exponent. We also argue that thermodynamical properties like the specific heat and the magnetocaloric effect (instead of the usual internal energy and the magnetization) can detect the mentioned quantum entanglement in solid systems. In addition, we suggest a tactic to find all critical temperatures, which is based on the derivative of the entanglement witness with respect to the temperature.

arXiv:1403.3437Physical Review AApr 8, 201439 citations

Entanglement in quantum-critical spin systems

Tommaso Roscilde, Paola Verrucchi, Andrea Fubini +2 more

arXiv:quant-ph/0412056Springer eBooksMay 29, 20061 citation

Effect of spin-orbit interaction on entanglement of two-qubit Heisenberg XYZ systems in an inhomogeneous magnetic field

Fardin Kheirandish, Seyed Javad Akhtarshenas, Hamidreza Mohammadi

The role of spin-orbit interaction in the ground state and thermal entanglement of a Heisenberg $XYZ$ two-qubit system in the presence of an inhomogeneous magnetic field is investigated. We show that the ground state entanglement tends to vanish suddenly for a certain value of the spin-orbit parameter $D$ and, when $D$ crosses its critical value ${D}_{c}$ , the entanglement undergoes a revival. Indeed, when $D$ crosses its critical value $({D}_{c})$ , the ground state entanglement tends to its maximum value $(C=1)$ . Also, at finite temperatures there are revival regions in the $D\text{\ensuremath{-}}T$ plane. In these regions, entanglement first increases with increasing temperature and then decreases and ultimately vanishes for temperatures above a critical value. We find that this critical temperature is an increasing function of $D$ and that the amount of entanglement in the revival region depends on the spin-orbit parameter. Therefore when spin-orbit interaction is included larger thermal entanglement can exist at higher temperatures. We also show that the rate of enhancement of thermal entanglement by $D$ is not the same for ferromagnetic $({J}_{z}<0)$ and antiferromagnatic $({J}_{z}>0)$ chains. The entanglement teleportation via the quantum channel constructed by the above system is also investigated, and the influence of the spin-orbit interaction on the fidelity of teleportation and entanglement of replica states is studied. We show that, by introducing spin-orbit interaction, the entanglement of the replica state and fidelity of teleportation can be increased for the case of ${J}_{z}<0$ . We also argue that a minimal entanglement of the channel is required to realize efficient entanglement teleportation and, in the case of ${J}_{z}<0$ , this minimal entanglement can be achieved by introducing spin-orbit interaction.The role of spin-orbit interaction in the ground state and thermal entanglement of a Heisenberg $XYZ$ two-qubit system in the presence of an inhomogeneous magnetic field is investigated. We show that the ground state entanglement tends to vanish suddenly for a certain value of the spin-orbit parameter $D$ and, when $D$ crosses its critical value ${D}_{c}$, the entanglement undergoes a revival. Indeed, when $D$ crosses its critical value $({D}_{c})$, the ground state entanglement tends to its maximum value $(C=1)$. Also, at finite temperatures there are revival regions in the $D\text{\ensuremath{-}}T$ plane. In these regions, entanglement first increases with increasing temperature and then decreases and ultimately vanishes for temperatures above a critical value. We find that this critical temperature is an increasing function of $D$ and that the amount of entanglement in the revival region depends on the spin-orbit parameter. Therefore when spin-orbit interaction is included larger thermal entanglement can exist at higher temperatures. We also show that the rate of enhancement of thermal entanglement by $D$ is not the same for ferromagnetic $({J}_{z}<0)$ and antiferromagnatic $({J}_{z}>0)$ chains. The entanglement teleportation via the quantum channel constructed by the above system is also investigated, and the influence of the spin-orbit interaction on the fidelity of teleportation and entanglement of replica states is studied. We show that, by introducing spin-orbit interaction, the entanglement of the replica state and fidelity of teleportation can be increased for the case of ${J}_{z}<0$. We also argue that a minimal entanglement of the channel is required to realize efficient entanglement teleportation and, in the case of ${J}_{z}<0$, this minimal entanglement can be achieved by introducing spin-orbit interaction.

arXiv:0801.1897Physical Review AApr 14, 2008105 citations

THERMAL ENTANGLEMENT IN SPIN SYSTEMS

N. Canosa, R. Rossignoli

Recent Progress in Many-Body TheoriesSep 1, 20060 citations

Thermal entanglement of spin chains with quantum critical behavior

Andrei A. Zvyagin

Results for the characteristics of the macroscopic thermal entanglement for integrable spin-1/2 antiferromagnetic chain models with multispin interactions in the thermodynamic limit are presented. Such interactions cause quantum-phase transitions to incommensurate phases with partial spontaneous magnetization. We have derived exact equations, which determine the thermal and magnetic field behavior of the concurrence of spin chains. The analysis of these equations shows that there exists a critical temperature, below which the thermal entanglement of considered spin chains is nonzero. We have shown that at those quantum-phase transitions, caused by multispin interactions, the thermal entanglement is reduced. Also, we have shown that the thermal entanglement is reduced due to nonzero magnetization of spin chains in the ground state, caused by multispin interactions.Results for the characteristics of the macroscopic thermal entanglement for integrable spin-1/2 antiferromagnetic chain models with multispin interactions in the thermodynamic limit are presented. Such interactions cause quantum-phase transitions to incommensurate phases with partial spontaneous magnetization. We have derived exact equations, which determine the thermal and magnetic field behavior of the concurrence of spin chains. The analysis of these equations shows that there exists a critical temperature, below which the thermal entanglement of considered spin chains is nonzero. We have shown that at those quantum-phase transitions, caused by multispin interactions, the thermal entanglement is reduced. Also, we have shown that the thermal entanglement is reduced due to nonzero magnetization of spin chains in the ground state, caused by multispin interactions.

Physical Review BOct 12, 200911 citations

Thermal entanglement in Spin-1 biparticle system

Guo‐Feng Zhang, Shu‐Shen Li, Liang Jiu-Qing

Optics CommunicationsNov 8, 200428 citations

The nearest-neighbor spins in the one-dimensional spin-1/2

XX

model with the added Dzyaloshinskii-Moriya (DM) interaction are entangled at zero temperature. In the presence of a transverse magnetic field (TF) they remain entangled up to a quantum critical field,

{h}_{c}

. Using the fermionization technique, we have studied the mutual effect of the DM interaction and a TF on the thermal entanglement (TE) in this model. The critical temperature where the entanglement disappears is specified. It is found that the TE in the finite-temperature neighborhood of the quantum critical field shows a scaling behavior with the critical exponent equal to the critical gap exponent. We also argue that thermodynamical properties like the specific heat and the magnetocaloric effect (instead of the usual internal energy and the magnetization) can detect the mentioned quantum entanglement in solid systems. In addition, we suggest a tactic to find all critical temperatures, which is based on the derivative of the entanglement witness with respect to the temperature.

The role of spin-orbit interaction in the ground state and thermal entanglement of a Heisenberg

XYZ

two-qubit system in the presence of an inhomogeneous magnetic field is investigated. We show that the ground state entanglement tends to vanish suddenly for a certain value of the spin-orbit parameter

D

and, when

D

crosses its critical value

{D}_{c}

, the entanglement undergoes a revival. Indeed, when

D

crosses its critical value

({D}_{c})

, the ground state entanglement tends to its maximum value

(C=1)

. Also, at finite temperatures there are revival regions in the $D\text{\ensuremath{-}}T$ plane. In these regions, entanglement first increases with increasing temperature and then decreases and ultimately vanishes for temperatures above a critical value. We find that this critical temperature is an increasing function of

D

and that the amount of entanglement in the revival region depends on the spin-orbit parameter. Therefore when spin-orbit interaction is included larger thermal entanglement can exist at higher temperatures. We also show that the rate of enhancement of thermal entanglement by

D

is not the same for ferromagnetic

({J}_{z}<0)

and antiferromagnatic

({J}_{z}>0)

chains. The entanglement teleportation via the quantum channel constructed by the above system is also investigated, and the influence of the spin-orbit interaction on the fidelity of teleportation and entanglement of replica states is studied. We show that, by introducing spin-orbit interaction, the entanglement of the replica state and fidelity of teleportation can be increased for the case of

{J}_{z}<0

. We also argue that a minimal entanglement of the channel is required to realize efficient entanglement teleportation and, in the case of

{J}_{z}<0

, this minimal entanglement can be achieved by introducing spin-orbit interaction.