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Chinese Physics B

Global entanglement in ground state of {Cu3} single-molecular magnet with magnetic field

Jiqiang Li, Bin Zhou

Published Jul 1, 2014• 1 citation
Publisher

Abstract

We investigate global entanglement in the ground state of single-molecular magnet Na 9 [Cu 3 Na 3 (H 2 O) 9 (α-AsW 9 O 33 ) 2 ]·26H 2 O with an external magnetic field. The concurrence, tangle, and measure function Q , which characterize the pairwise entanglement, 3-party entanglement and total entanglement, respectively, are calculated numerically at zero temperature. The results show that the magnitude and direction of the applied magnetic field play a significant role in the properties of three kinds of entanglement measures. We give a physical interpretation of the variation of the global entanglement with the magnetic field. Finally, the phase diagram of the global entanglement characterized by the critical magnetic fields is presented.

DOI
10.1088/1674-1056/23/7/070302

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We investigate global entanglement in the ground state of single-molecular magnet Na 9 [Cu 3 Na 3 (H 2 O) 9 (α-AsW 9 O 33 ) 2 ]·26H 2 O with an external magnetic field. The concurrence, tangle, and measure function Q , which characterize the pairwise entanglement, 3-party entanglement and total entanglement, respectively, are calculated numerically at zero temperature. The results show that the magnitude and direction of the applied magnetic field play a significant role in the properties of three kinds of entanglement measures. We give a physical interpretation of the variation of the global entanglement with the magnetic field. Finally, the phase diagram of the global entanglement characterized by the critical magnetic fields is presented.
We have investigated the properties of thermal entanglement in a triangular spin ring of the single molecular magnet (SMM) Na9[Cu3Na3(H2O)9 (α-AsW9O33)2]·26H2O in a magnetic field, and the pairwise concurrences of arbitrary two Cu2+ ion qubits are calculated numerically, hereafter abbreviated as C12, C23 and C13, respectively. Results show that the magnitude and direction of magnetic field as well as temperature have important effects on the pairwise thermal entanglement. Moreover, C12, C23 and C13 have difference variations with the change of the parameters. We also plot the changes of the critical temperatures Tc of C12, C23 and C13 with the magnetic fields along three different directions, and from the critical temperature-magnetic field phase diagrams one can obtain the ranges of parameters in which the pairwise thermal entanglement in a triangular spin ring of the SMM exists. Therefore, the pairwise entanglement can be controlled and enhanced in the SMM by choosing appropriate magnitude and direction of magnetic field and temperature.
Quantum entanglement is one of the most fundamental properties of quantum mechanics. Because of the nonlocality, quantum entanglement is widely used in quantum computation and quantum information. Considering the fact that thermal fluctuation suppresses quantum effects, the concept of thermal entanglement is introduced to refer to the idea that the effect of temperature should be viewed as external control in the preparation of entangled state. It has been found that nanoscale single molecular magnet has a novel quantum effect at low temperature. Furthermore, single-molecular magnet is viewed as a promising candidate for realizing encoding and manipulation of quantum information. Na9[Cu3Na3(H2O)9(-AsW9O33)2]26H2O (denoted as {Cu3} for convenience) is one of the typical representatives of nanoscale single molecular magnets. In this paper, we will theoretically analyze the properties of tripartite entanglement in {Cu3} with an external magnetic field in thermal equilibrium. The tripartite negativity is used to characterize the tripartite entanglement. The tripartite negativity of {Cu3} single molecular magnet is calculated numerically by using the equivalent spin model and experimental fitting parameters. We consider the magnetic fields along the vertical and the parallel directions of triangular spin ring, respectively, and the case with a tilted magnetic field is also discussed in this paper. It is shown that the magnitude and direction of magnetic field, and temperature have importance effects on the tripartite negativity of the system. It is found that the larger extra strong magnetic field will inhibit the generation of the quantum state of tripartite entanglement at higher temperature. In addition, compared with the magnetic field along the parallel direction of triangular spin ring and the tilted magnetic field, the magnetic field along the vertical direction of triangular spin ring obtains larger values of tripartite negativity under the same temperature and magnetic field. We also plot the variations of the critical temperature with the magnetic field along different directions, and from the critical temperature-magnetic field phase diagrams one can obtain the range of parameters in which the tripartite entanglement of the system exists. We also find that entanglement revival behaviors may occur in the specific range of parameters. Therefore, the properties of the tripartite entanglement in the {Cu3} triangular spin ring can be controlled and enhanced by choosing appropriate magnitude and direction of the magnetic field and temperature.
We study the entanglement properties of a molecular three-qubit system described by the Heisenberg spin Hamiltonian with anisotropic exchange interactions and including an external magnetic field. The system exhibits first-order quantum phase transitions by tuning two parameters, x and y, of the Hamiltonian to specific values. The three-qubit chain is open-ended so that there are two types of pairwise entanglement: nearest-neighbour (nn) and next-nearest-neighbour (nnn). We calculate the ground and thermal state concurrences, quantifying pairwise entanglement, as a function of the parameters x, y and the temperature T. The entanglement threshold and gap temperatures are also determined as a function of the anisotropy parameter x. The results obtained are of relevance in understanding the entanglement features of the recently engineered molecular Cr(7)Ni-Cu(2+)-Cr(7)Ni complex which serves as a three-qubit system at sufficiently low temperatures.
We study the entanglement properties in a one-dimensional Ising chain with a tilted magnetic field that is capable of showing both integrable and nonintegrable behaviors. Here the pairwise entanglement is characterized by concurrence and the multipartite entanglement is characterized by the Q measure. According to the entanglement properties of the ground state in the Ising mode, which have tilt angle, we can find that the Q measure decreases with the increasing of the strength of external field. And the phase transition property of the system is changed with the increase of tilt angle for the external magnetic field. We also consider the evolution of entanglement in this model, and find that the nonintegrability can suppress the pairwise entanglement but promotes the multipartite entanglement with the integrable system.
The entanglement and quantum correlation measures have been investigated for the ground state of a spin chain with a Kitaev-type exchange interactions on alternating bonds, along with a transverse magnetic field. There is a macroscopic degeneracy in the ground state for zero magnetic field, implying a quantum critical point. In this model, many entanglement and correlation measures, except the macroscopic multispecies entanglement measure, do not show true singular behavior in the vicinity of the critical point, as seen in the transverse-Ising model ground state and related models. We compute the pair concurrence measure of entanglement, the pair quantum discord to track the quantum correlations, and a global entanglement measure and a multispecies entanglement measure to investigate multiparty entanglement, both analytically and numerically. The nearest-neighbor concurrence shows a peak structure as a function of magnetic field, near the critical point, for various values of the ratio of interaction strengths, but its derivative does not show a singular behavior close to the critical point. A similar behavior is shown by the quantum discord and the global entanglement. The multispecies entanglement shows a clear signature of the critical point behavior, and the first-order derivative shows a divergence near zero magnetic field, for equal interaction strengths.
The entanglement at zero-temperature is studied in a two-qubit XZ spin-1/2 chain model in an external magnetic field which is applied in the z direction. We have obtained an analytical relation for the effect of the external magnetic field on the concurrence. It is shown that the ground state of the system depends on the strength of exchange coupling. We have shown that the analytical relation of the concurrence is independent of Jz. It is shown that for Jz >0 the concurrence is depended on the critical value of the external magnetic field and it is changed at the critical external magnetic field. Also we have shown that for h hc, the concurrence decreases by increasing the external magnetic field. For Jz <0, the concurrence decreases by increasing the external magnetic field.