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arXiv:1911.04754 · Acta Physica Polonica A

Pairwise Entanglement in Double-Tetrahedral Chain with Different Landé g-Factors of the Ising and Heisenberg Spins

Lucia Gálisová

Published May 1, 2020• 3 citations
arXivHTMLPDF

Abstract

The pairwise entanglement is exactly examined in the spin-1/2 Ising-Heisenberg double-tetrahedral chain with different Landé g-factors of the Ising and Heisenberg spins at zero and finite temperatures.It is shown that the phenomenon present in quantum non-chiral ground states is twice as strong as in quantum chiral ground states and that it gradually diminishes with increasing temperature until it completely vanishes at a certain threshold temperature.It is also demonstrated that the strong magnetic field maintains a weak thermal entanglement quite far from the saturation field, although the ground state is non-entangled.

DOI
10.12693/aphyspola.137.604

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The pairwise entanglement is exactly examined in the spin-1/2 Ising-Heisenberg double-tetrahedral chain with different Landé g-factors of the Ising and Heisenberg spins at zero and finite temperatures.It is shown that the phenomenon present in quantum non-chiral ground states is twice as strong as in quantum chiral ground states and that it gradually diminishes with increasing temperature until it completely vanishes at a certain threshold temperature.It is also demonstrated that the strong magnetic field maintains a weak thermal entanglement quite far from the saturation field, although the ground state is non-entangled.
Typically two particles (spins) could be maximally entangled at zero temperature, and for a certain temperature the phenomenon of entanglement vanishes at the threshold temperature. For the Heisenberg coupled model or even the Ising model with a transverse magnetic field, one can observe some rise of entanglement even for a disentangled region at zero temperature. So we can understand this emergence of entanglement at finite temperature as being due to the mixing of some maximally entangled states with some other untangled states. Here, we present a simple one-dimensional Ising model with alternating Ising and Heisenberg spins in an arbitrarily oriented magnetic field, which can be mapped onto the classical Ising model with a magnetic field. This model does not show any evidence of entanglement at zero temperature, but surprisingly at finite temperature rise a pairwise thermal entanglement between two untangled spins at zero temperature when an arbitrarily oriented magnetic field is applied. This effect is a purely magnetic field, and the temperature dependence, as soon as the temperature increases, causes a small increase in concurrence, achieving its maximum at around 0.1. Even for long-range entanglement, a weak concurrence still survives. There are also some real materials that could serve as candidates that would exhibit this effect, such as Dy(NO3{}_{3}3​)(DMSO)2{}_{2}2​Cu(opba)(DMSO)2{}_{2}2​ [DMSO = dimethyl sulfoxide; opba = ooo-phenylenebis(oxamoto)] [J. Stre\ifmmode \check{c}\else \v{c}\fi{}ka, M. Hagiwara, Y. Han, T. Kida, Z. Honda, and M. Ikeda, Condens. Matter Phys. 15, 43002 (2012)].
We study the entanglement of thermal and ground states in the Heisenberg XY spin chain with an inhomogeneous magnetic field.A general result is found that for two-qubit case,pairwise entanglement is independent of the sign of coupling constant J,magnetic field B,anisotropic parameter γ and inhomogeneous parameter b of the magnetic field.At zero absolute temperature,an analytical expression of concurrence C is given through which we show that the critical magnetic field Bc increases with the increase of inhomogeneity.At finite temperature,we show analytically for the isotropic case and numerically for the anisotropic case that the thermal entanglement can be apparently enhanced by introducing the inhomogeneity of the magnetic field.We also show that for isotropic case the critical temperature Tc is alone an increasing function of the inhomogeneous parameter b,while for anisotropic case,it is determined by both B and b.
The spin-1/2 Ising-Heisenberg trimerized chain in a magnetic field is revisited with the aim to explore the quantum entanglement and non-locality within the exactly solved spin system, which exhibits in a low-temperature magnetization curve two intermediate plateaux at zero and one-third of the saturation magnetization.The groundstate phase diagram involves two quantum (antiferromagnetic, ferrimagnetic I) and two classical (ferrimagnetic II, saturated paramagnetic) phases.We have rigorously calculated the concurrence and Bell function in order to quantify the quantum entanglement and non-locality at zero as well as non-zero temperatures.It is demonstrated that the entanglement can be thermally induced also above the classical ground states unlike the quantum nonlocality, which means that the thermal entanglement is indispensable for a violation of the locality principle.
The thermal pairwise entanglement (TE) of the S=1/2S=1/2S=1/2 XYXYXY chain in a transverse magnetic field is exactly resolved by means of the Jordan-Wigner transformation in the thermodynamic limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$. It is found that the TE vanishes at a fixed point with temperature ${T}_{c}\ensuremath{\simeq}0.484\text{ }3J$, which is independent of the magnetic field. A thermal quantity is proposed to witness the entangled state. Furthermore, the TE of the S=1/2S=1/2S=1/2 antiferromagnetic-ferromagnetic (AF-F) Heisenberg chain is studied by the transfer-matrix renormalization-group method. The TEs of the spins coupled by AF and F interactions are found to behave distinctively. The vanishing temperature of the field-induced TE of the spins coupled by F interactions is observed dependent on the magnetic field. The results are further confirmed and analyzed within a mean-field framework.
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 properties of a three-spin XXZ Heisenberg chain with three-spin interaction are studied by means of concurrence of pairwise entanglement. We show that ground-state pairwise entanglement, pairwise thermal entanglement, or quantum phase transition is not present in antiferromagnetic spin chain. For the ferromagnetic case, quantum phase transition takes place at Δ = 1 for anisotropic interaction and at some values of three-spin coupling strength, and pairwise thermal entanglement increases when the value of J / T increases and with anisotropic interaction and three-spin interaction decrease. In addition, we find that increasing the anisotropic interaction and the three-spin interaction will decrease critical temperature.