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International Journal of Quantum Information

Thermal entanglement in a mixed spin Heisenberg XXX chain with DM interaction

Nizar Ahami, M. El Baz

Published Aug 1, 2021• 6 citations

Abstract

We consider a one-dimensional, mixed spin Heisenberg XXX model with an homogeneous external magnetic field and Dzyaloshinskii–Moriya interaction. Alternating spin-[Formula: see text] and spin-1 particles are forming the chain. The effect of the different parameters of the system on the bipartite thermal entanglement is studied. The type of chain used (mixed) and the size of the chain ([Formula: see text]) allow to study three types of bipartite entanglement, the qubit–qubit, qubit–qutrit and qutrit–qutrit thermal entanglement.

DOI: 10.1142/s0219749921500210

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We consider a one-dimensional, mixed spin Heisenberg XXX model with an homogeneous external magnetic field and Dzyaloshinskii–Moriya interaction. Alternating spin-[Formula: see text] and spin-1 particles are forming the chain. The effect of the different parameters of the system on the bipartite thermal entanglement is studied. The type of chain used (mixed) and the size of the chain ([Formula: see text]) allow to study three types of bipartite entanglement, the qubit–qubit, qubit–qutrit and qutrit–qutrit thermal entanglement.

We analytically investigate the thermal entanglement of three-mixed-spin (1/2, 1, 1/2) XXZ model with the DM interaction under an external magnetic field B. Two different cases are considered: one subsystem (1/2, 1/2) consists of two spin-1/2 fermions and the other subsystem (1/2, 1) contains a spin-1/2 fermion and a spin-1 boson. It is shown that the DM interaction parameter D, the external magnetic field strength B and coupling constant J have different effects on Fermi and mixed Fermi–Bose systems. All of the factors mentioned above can be utilized to control entanglement switch of any two particles in mixed spins model.

The effects of the different Dzyaloshinskii—Moriya (DM) interaction on thermal entanglement of a two-qutrit Heisenberg XX spin chain in a nonuniform magnetic field are investigated. Our results imply that the x-component DM interaction plays a central role in enhancing quantum entanglement and it has a higher critical temperature than the z-component DM interaction. The entanglement can be tunable controlled by changing the multiple of the magnetic fields B 1 and B 2 . Also we found that different DM interaction are competitive to each other in some conditions.

In this paper, we study the improvement and manipulation of pairwise thermal entanglement in one-dimentional three-qubit Heisenberg model, where Dzyaloshinskii-Moriya （DM） interaction is considered and concurrence is calculated to research this entanglements property. The results show that for XXX model, DM interaction can induce entanglement in the antiferromagnetic and ferromagnetic spin chains although the required critical values are different for these cases. For XXZ model, by introducing DM interaction D, antiferromagnetic spin chain has entanglement which is absent when D=0, and in addition, for antiferromagnetic and ferromagnetic cases, DM interaction D and the anisotropy parameter Δ have different effects on entanglement. As a result, the entanglement can be controlled and enhanced by choosing appropriate DM interaction and anisotropy parameter. Furthermore, we find that at the same temperature, no matter for antiferromagnetic or ferromagnetic spin chains, the critical DM interaction inducing entanglement should be greater in a three-qubit XXZ model than that in a two-qubit XXZ model.

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 .

In the present work, initially, a mixed-three-spin (1/2,1,1/2) cell of a mixed-[Formula: see text]-spin chain with Ising-XY model is introduced, for which pair spins (1,1/2) have Ising-type interaction and pair spins (1/2,1/2) have both XY-type and Dzyaloshinskii–Moriya (DM) interactions together. An external homogeneous magnetic field [Formula: see text] is considered for the system in thermal equilibrium. Integer-spins have a single-ion anisotropy property with coefficient [Formula: see text]. Then, we investigate the quantum entanglement between half-spins (1/2,1/2), by means of the concurrence. Classical correlation (CC) for this pair of spins is investigated as well as the concurrence and some interesting temperature, the magnetic field and the DM interaction properties are expressed. Moreover, single-ion anisotropy effects on the correlation between half-spins is verified. According to the verifications based on the communication channels category by Rossini, Giovannetti and Fazio [D. Rossini, V. Giovannetti and R. Fazio, Int. J. Quantum Inf. 5, 439 (2007)], we theoretically consider such tripartite spin model as an ideal quantum channel, then calculate its information transmission rate and express some differences in behavior between this suggested model and introduced simple models in the previous works (chains without spin integer and DM interaction) from information transferring protocol point of view.

Thermal pairwise entanglement of a three-qubit Heisenberg XX chain with the Dzyaloshinski-Moriya(DM) anisotropic antisymmetric interaction under an external magnetic field and quantum teleportation when using the Heisenberg chain as a channel are investigated.The entanglement and fidelity depending on the DM interaction,magnetic field and temperature are given in detail.The results show that the thermal entanglement can be controlled by magnetic field and DM interaction.Quantum teleportation will be better realized via an ferromagnetic spinchain when the DM interaction and external magnetic field are turned off and the temperature is low.The thermal entanglement cannot completely reflect the teleportation fidelity,and the same thermal entanglement could yield different average teleportation fidelities.