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Chinese Physics B

Entanglement in a two-spin system with long-range interactions

Mohammad Reza Soltani, S. Mahdavifar, Maryam Mahmoudi

Published Jul 26, 2016• 10 citations
Publisher

Abstract

The quantum entanglement between two spins in the Ising model with an added Dzyaloshinsky–Moriya (DM) interaction and in the presence of the transverse magnetic field is studied. The exchange interaction is considered as a function of the distance between spins. The negativity as a function of magnetic field, exchange and DM interaction is calculated. The effect of the distance between spins is studied based on the negativity. In addition, the effect of the thermal fluctuation on the negativity is also investigated.

DOI
10.1088/1674-1056/25/8/087501

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The quantum entanglement between two spins in the Ising model with an added Dzyaloshinsky–Moriya (DM) interaction and in the presence of the transverse magnetic field is studied. The exchange interaction is considered as a function of the distance between spins. The negativity as a function of magnetic field, exchange and DM interaction is calculated. The effect of the distance between spins is studied based on the negativity. In addition, the effect of the thermal fluctuation on the negativity is also investigated.
Thermal entanglement of a two-qubit Ising chain subjected to an external magnetic field and Dzyaloshinsky—Moriya (DM) interaction is examined. The effect of magnetic field, strength of DM interaction and temperature are analyzed by adopting negativity of partial transpose as the measure of entanglement. It is shown that when the DM interaction along the Ising axis is considerable, thermal entanglement can be sustained for a higher temperature. The usefulness of longitudinal DM interaction over the one that is perpendicular to the Ising axis, in the manipulation and control of entanglement at a feasible temperature, is illustrated.
Taking Dzyaloshinskii-Moriya(DM)effect interaction into account,the entanglement of two-qubit Ising model in an inhomogeneous magnetic field is investigated by means of Negativity theory.It is shown that the existence of DM interaction can obviously enhance the entanglement and put it into a maximum while the magnetic field reduces the entanglement.In addition,low temperature also plays a positive role in entanglement.Moreover,the influence of inhomogeneous magnetic field is also investigated. These effects indicate that one can control the thermal entanglement by manipulation of DM interaction, the homogeneous and inhomogeneous magnetic field and temperature.
The effects of Dzyaloshinskii-Moriya (DM) interaction on the thermal entanglement of mixed-spin XY chain (1/2,3/2) and spin 1 XY chain are investigated through negativity. By calculating the entanglement between two particles, it was found that the DM interaction can not only increase the entanglement, but also make the entanglement of the particles reach a stationary value. The higher the temperature, the greater the DM interaction is required to make the thermal entanglement arrive at this stationary value. Under the same condition, the entanglement between two spin 1 particles is less than that between mixed-spin. The exchange-coupling interactions between the spins are helpful to strengthen the thermal entanglement, hence the exchange-coupling can be used to modulate the entanglement along with the DM interaction. When the exchange-coupling interaction is small, one can enlarge the DM interaction to increase the entanglement, whereas, when the DM interaction is small, one can increase the thermal entanglement through increasing the exchange-coupling interaction.
The negativity ( N ) as a measure of thermal entanglement (TE) is studied for a two-qutrit spin-1 anisotropic Heisenberg XXZ chain with Dzyaloshinskii—Moriya (DM) interaction in an inhomogeneous magnetic field in detail. The effects of the DM interaction parameter D z on the thermal variation of the N for given values of the external magnetic field B , a parameter b which controls the inhomogeneity of B and the bilinear interaction parameters J x = J y ≠ J z are obtained. It is found that N persists to higher values and to higher temperatures for the higher values of ± D z and for the higher positive values of J z , i.e. in the antiferromagnetic (AFM) case. When J z < 0, the ferromagnetic (FM) case, and D z is small, and if J z is strong enough to compete with D z , N decreases. In addition, N declines with the increasing values of B and b .
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 .