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TURKISH JOURNAL OF PHYSICS

Localizable entanglement of isotropic antiferromagnetic spin-1/2 chain

İzzet Paruğ Duru, S. Aktas

Published Jun 12, 2019• 1 citation
Publisher

Abstract

The bounds of entanglement on antiferromagnetic (AF) isotropic Heisenberg spin-1/2 chain including dipole- dipole interaction (D) were investigated. The Quantum Monte Carlo method based on loop algorithm was employed to calculate the two-spin and single-spin expectation values mediating the lower and upper bounds. It was revealed that D and Bz (the applied magnetic field) were pivotal parameters in controlling either entanglement creation/extinction or entanglement enhancement/weakening. Rival regions indicated a revival phenomenon depending on the temperature for various strengths of D which also showed a nonmonotonic behavior under certain Bz identifying critical points. Even if thermal agitations break the stability of strong D entanglement, it remains invariable at very low temperatures.

DOI
10.3906/fiz-1812-26

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The bounds of entanglement on antiferromagnetic (AF) isotropic Heisenberg spin-1/2 chain including dipole- dipole interaction (D) were investigated. The Quantum Monte Carlo method based on loop algorithm was employed to calculate the two-spin and single-spin expectation values mediating the lower and upper bounds. It was revealed that D and Bz (the applied magnetic field) were pivotal parameters in controlling either entanglement creation/extinction or entanglement enhancement/weakening. Rival regions indicated a revival phenomenon depending on the temperature for various strengths of D which also showed a nonmonotonic behavior under certain Bz identifying critical points. Even if thermal agitations break the stability of strong D entanglement, it remains invariable at very low temperatures.
The quantum entanglement of mixed XXZ Heisenberg spin-1/2 chain is examined. We quantify localizable entanglement (LE) in terms of upper/lower bounds through Quantum Monte Carlo simulations. Loop algorithm is chosen to numerically calculate thermodynamic quantities including spin-spin correlations. The exchange coupling, Zeeman energy, and dipolar interaction are literally taken into account. Findings summarize that the strength of dipole-dipole interaction (D) and external magnetic field (Bz) are notable in entanglement formation driving creation and extinction of entanglement. The creation and extinction of entanglement depend on D and Bz. Furthermore, strong fields at the critical temperatures lead a non-monotonic/monotonic behavior introducing revival phenomena. Nevertheless, strong D provides the distance-dependent stability of LE values, preserving unity.
The entanglement of the ferromagnetically ordered isotropic spin-1/2 chain is discussed. The analytically deriving concurrence of a two-qubit state allows focusing on the effect of dipolar interaction (D). Low fields enable tuning creation/extinction of entangled states, particularly at low temperatures. There is a joint effect of the applied field and dipolar interaction which can’t be disregarded. We perform Quantum Monte Carlo simulations on quantifying localizable entanglement (LE) in terms of upper/lower bounds. Findings reveal that D and B_z are decisive parameters on the production of entanglement including creation and extinction. A non-monotonic behavior has occurred under high fields at the critical temperature. However, strong D provides the stability of LE values concerning distance herewith conserving the unity at low temperatures under zero field. Rival regions are observed for the distant nearest neighbors, particularly odd ones.
Thermal entanglement of a two-qubit Heisenberg XYZ chain is studied.It is found that the ground state entanglement maintains a maximal constant until it drops suddenly at a critical magnetic field.Increasing the value of can extend the entanglement region in terms of temperature and magnetic field.At a finite temperature,increasing the anisotropy parameter can enhance and extend the revival entanglement when the magnetic field is beyond the critical point.These results may provide theoretical proof for manipulating the entanglement with magnetic field,strength of interaction and anisotropy parameter.
The entanglement quantum properties of a spin-1/2 Ising-Heisenberg model on a symmetrical diamond chain were analyzed. Due to the separable nature of the Ising-type exchange interactions between neighboring Heisenberg dimers, calculation of the entanglement can be performed exactly for each individual dimer. Pairwise thermal entanglement was studied in terms of the isotropic Ising-Heisenberg model and analytical expressions for the concurrence (as a measure of bipartite entanglement) were obtained. The effects of external magnetic field H and next-nearest neighbor interaction J(m) between nodal Ising sites were considered. The ground state structure and entanglement properties of the system were studied in a wide range of coupling constant values. Various regimes with different values of ground state entanglement were revealed, depending on the relation between competing interaction strengths. Finally, some novel effects, such as the two-peak behavior of concurrence versus temperature and coexistence of phases with different values of magnetic entanglement, were observed.
In the study of thermal entanglement of the Heisenberg spin chain model, one usually considers only the spin interaction between the nearest neighboring qubits. Actually, a generalized Heisenberg model, so-called J1-J2 Heisenberg model, which is constructed by considering the fact that not only the nearest neighboring but also the next nearest neighboring spin interaction also plays an important role. In J1-J2 Heisenberg model, due to the next nearest neighboring spin interaction, the frustration effect can occur and has an important influence on the magnetic properties of the model. In this paper we investigate the thermal entanglement of a five-qubit XXZ Heisenberg spin chain with the next nearest neighboring interaction in a magnetic field. Using the numerical method, we calculate the pairwise concurrences of the nearest neighbouring qubits and the next nearest neighboring qubits, abbreviated as C12 and C13 respectively. The numerical results show that the frustration parameter α has an important effect on the pairwise thermal entanglement. Moreover, C12 and C13 have different variations with the change of the frustration parameter α. Meanwhile, it is found that the temperature, magnetic field, Dzyaloshinkii-Moriya (DM) interaction and anisotropic parameter also have great effects on the thermal entanglement. The increasing of temperature can reduce the thermal entanglement. The magnetic field can enhance the thermal entanglement between both two nearest and next nearest neighboring qubits, but when the magnetic field becomes strong enough, only the thermal entanglement between the two nearest neighboring qubits is suppressed. A certain extent of DM interaction can enhance the thermal entanglement between the two nearest neighboring qubits. But for the next nearest neighboring qubits, without the magnetic field, the increasing of DM interaction mainly enlarge the entanglement vanishing area of frustration parameter α. When the system changes from anisotropic to isotropic state, the entanglement vanishing area also changes obviously for C12 and C13. Thus, we can choose appropriate magnetic field strength, temperature, frustration parameter, DM interaction parameter and anisotropic parameter to effectively control and enhance the thermal entanglement of the system.
Quantum phase transition in dimerized antiferromagnetic Heisenberg spin chain has been studied. A staircase structure in the variation of concurrence within strongly coupled pairs with that of external magnetic field has been observed indicating multiple critical points. Emergence of entanglement due to external magnetic field or magnetic entanglement is observed for weakly coupled spin pairs in the same dimer chain. Though closed dimerized isotropic XXX Heisenberg chains with different dimer strengths were mainly explored, analogous studies on open chains as well as closed anisotropic (XX interaction) chains with tilted external magnetic field have also been studied.