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Journal of Contemporary Physics (Armenian Academy of Sciences)

Quantum Entanglement in Spin Dimers: Effects of a Magnetic Field and Heterogeneous g-Factors

Zhirayr Adamyan, S. A. Muradyan, Vadim Ohanyan

Published Oct 1, 2020• 9 citations
Publisher

Abstract

Abstract This work considers the spin-1/2 Heisenberg dimer, the mixed spin-(1/2,1) Heisenberg dimer and their quantum entanglement, particularly, the dependence of the entanglement on the system characteristics and the external magnetic field. The quantum entanglement in this work is determined using two different methods, namely ‘Negativity’ and ‘Concurrence’. The dependence of the corresponding quantities on spins Landé g-factors, system anisotropy constants and exchange constant is discussed.

DOI
10.3103/s1068337220040027

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•Jul 8, 2021•0 citations
Abstract This work considers the spin-1/2 Heisenberg dimer, the mixed spin-(1/2,1) Heisenberg dimer and their quantum entanglement, particularly, the dependence of the entanglement on the system characteristics and the external magnetic field. The quantum entanglement in this work is determined using two different methods, namely ‘Negativity’ and ‘Concurrence’. The dependence of the corresponding quantities on spins Landé g-factors, system anisotropy constants and exchange constant is discussed.
Mixed spin-(1/2,1/2,1) trimer with two different Landé g factors and two different exchange couplings is considered. The main feature of the model is nonconserving magnetization. The Hamiltonian of the system is diagonalized analytically. We presented a detailed analysis of the ground-state properties, revealing several possible ground-state phase diagrams and magnetization profiles. The main focus is on how nonconserving magnetization affects quantum entanglement. We have found that nonconserving magnetization can bring a continuous dependence of the entanglement quantifying parameter (negativity) on the magnetic field within the same eigenstate, while for the case of uniform g factors it is a constant. The main result is an essential enhancement of the entanglement in the case of uniform couplings for one pair of spins caused by an arbitrary small difference in the values of g factors. This enhancement is robust and brings almost a sevenfold increase of the negativity. We have also found a weakening of entanglement for other cases. Thus, nonconserving magnetization offers a broad opportunity to manipulate the entanglement by means of a magnetic field.
Heisenberg model spin systems offer favourable and manageable physical settings for generating and manipulating entangled quantum states. In this work mixed spin-(1/2,1/2,1) Heisenberg spin trimmer with two different but isotropic Landé g-factors and two different exchange constants is considered. The study undertakes the task of finding the optimal parameters to create entangled states and control them by external magnetic field. The primary objective of this work is to examine the tripartite entanglement of a system and the dependence of the tripartite entanglement on various system parameters. Particularly, the effects of non-conserving magnetization are in the focus of our research. The source of non-commutativity between the magnetic moment operator and the Hamiltonian is non-uniformity of g-factors. To quantify the tripartite entanglement, an entanglement measure refered to as “tripartite negativity” has been used in this work.
A genuine tripartite entanglement of a mixed spin-(1/2,1) Heisenberg tetramer is rigorously analyzed in a presence of external magnetic field. The couple of mixed spin-(1/2,1) dimers is arranged in a perfect rectangular square plaquette involving two nonequivalent Heisenberg exchange couplings JJJ and J1J_1J1​. The degree of a genuine tripartite entanglement is evaluated according to the genuine tripartite negativity NABC{\cal N}_{ABC}NABC​ defined as a geometric mean of all possible bipartite negativities corresponding to a decomposition into a single spin and the remaining spin dimer NA∣BC{\cal N}_{A|BC}NA∣BC​, NB∣AC{\cal N}_{B|AC}NB∣AC​ and NC∣AB{\cal N}_{C|AB}NC∣AB​ after degrees of freedom of the last fourth spin DDD are traced out. Due to the symmetry of a mixed spin-(1/2,1) Heisenberg tetramer two different genuine tripartite negativities for the trimeric system 1/2 ⁣− ⁣1 ⁣− ⁣11/2\!-\!1\!-\!11/2−1−1 and 1/2 ⁣− ⁣1/2 ⁣− ⁣11/2\!-\!1/2\!-\!11/2−1/2−1 were identified. It was found that the genuine tripartite negativity for the interaction ratio J1/J ⁣< ⁣1J_1/J\!<\!1J1​/J<1 becomes nonzero solely in the tripartite system 1/2 ⁣− ⁣1 ⁣− ⁣11/2\!-\!1\!-\!11/2−1−1 at low-enough magnetic fields. The opposite interaction limit J1/J ⁣> ⁣1J_1/J\!>\!1J1​/J>1 gives rise to the nonzero genuine tripartite negativity in both tripartite systems in a presence of external magnetic field until the classical ferromagnetic state is achieved. It was shown, that the genuine tripartite negativity of a mixed spin-(1/2,1) Heisenberg tetramer can be detected also at nonzero temperatures. An enhancement of the thermal genuine tripartite negativity through the enlargement of the total spin number of a tripartite system is evidenced. The correlation between the bipartite negativity of two spins and the genuine tripartite negativity is discussed in detail.
In contrast to the spin-half Heisenberg model, we investigate the effects of anisotropy and external magnetic field on thermal entanglement in a (1/2,1) mixed-spin Heisenberg model. By using the concept of negativity, we find the critical temperature T c and critical magnetic field B c of mixed-spin are much higher than that of spin-half, and this phenomenon is more evident with increasing anisotropy coefficient Δ. Contrary to the spin-half, we also observe that the nonuniform field can enhance the entanglement of mixed-spin to a great extent.
The entanglement thermal (equilibrium) properties in spin-1/2 Ising-Heisenberg model on an ideal diamond chain is analyzed. Due to the classical character of Ising-type exchange interactions between two neighboring antiferromagnetic Heisenberg dimers, the calculation of quantum entanglement (by tracing out Ising spins) can be performed for each of the dimers separately. The concurrence, as a measure of entanglement is obtained and different regimes depending on the values of exchange interactions are revealed. The effects of the magnetic field are incorporated and critical temperatures corresponding to the vanishing or arising of entanglement are considered.
The quantum and thermal entanglement in the mixed spin-(1/2,SSS) Heisenberg dimer with an uniaxial single-ion anisotropy
The concept of negativity is used to study the quantum and thermal entanglement in a generalized spin-(1/2,SSS) Heisenberg dimer under presence of an external magnetic field. The competition effect of interplay between the spin diversity, XXZ exchange as well as uniaxial single-ion anisotropy is additionally analysed with a goal to tune the degree and thermal stability of the pairwise entanglement. Obtained analytical results favour the antiferromagnetic spin-(1/2,SSS) Heisenberg dimer instead of the ferromagnetic one, where the higher degree of entanglement and higher threshold temperature are achieved at the same set of model parameters. It is demonstrated and analytically proven that the increasing magnitude of spin SSS in dimer with an easy-axis uniaxial single-ion anisotropy can enhance not only the thermal stability but simultaneously the degree of entanglement. It is shown additionally, that the further enhancement of entanglement can be improved in dimer with a half-odd-integer spin SSS as a consequence of different magnetic ground-states. In such system the low-enough thermal negativity saturates in its maximal value regardless the magnitude of half-odd-integer spin SSS. Because of the influence of the magnetic-field induced consecutive second-order phase transitions in dimer with S ⁣> ⁣1S\!>\!1S>1, the surprising oscillating behaviour of negativity upon the magnetic field is observed at low-enough temperature.