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Physica A Statistical Mechanics and its Applications

Numerical transfer-kernel results for a classical spin chain with anisotropic exchange interaction and a magnetic field

Thomas Delica, Hajo Leschke

Published Oct 1, 1990• 5 citations
Publisher
DOI
10.1016/0378-4371(90)90029-r

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Two Qubit Entanglement in XYZXYZXYZ Magnetic Chain with DM Antisymmetric Anisotropic Exchange Interaction
In the present paper we study two qubit entanglement in the most general XYZXYZXYZ Heisenberg magnetic chain with (non)homogeneous magnetic fields and the DM anisotropic antisymmetric exchange interaction, arising from the spin-orbit coupling . The model includes all known results as particular cases, for both antiferromagnetic and ferromagnetic XX,XY,XXX,XXZ,XYZXX, XY, XXX, XXZ, XYZXX,XY,XXX,XXZ,XYZ chains. The concurrence of two qubit thermal entanglement and its dependence on anisotropic parameters, external magnetic field and temperature are studied in details. We found that in all cases, inclusion of the DM interaction, which is responsible for weak ferromagnetism in mainly antiferromagnetic crystals and spin arrangement in low symmetry magnets, creates (when it does not exist) or strengthens (when it exists) entanglement in XYZXYZXYZ spin chain. This implies existence of a relation between arrangement of spins and entanglement, in which the DM coupling plays an essential role. It suggests also that anisotropic antisymmetric exchange interaction could be an efficient control parameter of entanglement in the general XYZXYZXYZ case.
We numerically investigate the critical behavior of the spin-(1,12)(1,\frac{1}{2})(1,21​) Heisenberg ferrimagnet with anisotropic exchange coupling in a magnetic field. A quantized magnetization plateau as a function of the field, appearing at a third of the saturated magnetization, is stable over the whole antiferromagnetic coupling region. The plateau vanishes in the ferromagnetic coupling region via the Kosterlitz-Thouless transition. Comparing the quantum and classical magnetization curves, we elucidate what are essential quantum effects.
In this work, we use the Hamiltonian of a modified Dzyaloshinskii-Moriya model and investigate the perfect transfer of the quantum state on the spin networks. In this paper, we calculate fidelity in which fidelity depends on magnetic field and another parameters. Then, by using the numerical analysis we show that the fidelity of the transferred state is determined by magnetic field BBB, exchange coupling JJJ and the Dzyaloshinskii- Moriya interaction DDD. We also found that the perfect transfer of the quantum state is possible with condition B≫Γ2ωN/2B \gg Γ^2ω^{N/2}B≫Γ2ωN/2 where Γ=((J+iD)/2)Γ=((J+iD)/2)Γ=((J+iD)/2) and ω=Γ∗/Γω=Γ^*/ Γω=Γ∗/Γ.