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Acta Physica Sinica

Properties of entanglement in one-dimensional Ising model with a tilted magnetic field

Wang Qi, Xiaoqian Wang

Published Jan 1, 2013• 0 citations
Publisher

Abstract

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.

DOI
10.7498/aps.62.220301

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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.
We study a one-dimensional Ising model with a magnetic field and show that tilting the field induces a transition to quantum chaos. We explore the stationary states of this Hamiltonian to show the intimate connection between entanglement and avoided crossings. In general, entanglement gets exchanged between the states undergoing an avoided crossing with an overall enhancement of multipartite entanglement at the closest point of approach, simultaneously accompanied by diminishing two-body entanglement as measured by concurrence. We find that both for stationary as well as nonstationary states, nonintegrability leads to a destruction of two-body correlations and distributes entanglement more globally.
We study multipartite entanglement measures for a one-dimensional Ising chain that is capable of showing both integrable and nonintegrable behavior. This model includes the kicked transverse Ising model, which we solve exactly using the Jordan-Wigner transform, as well as nonintegrable and mixing regimes. The cluster states arise as a special case and we show that while one measure of entanglement is large, another measure can be exponentially small, while symmetrizing these states with respect to up and down spins produces those with large entanglement content uniformly. We also calculate exactly some entanglement measures for the nontrivial but integrable case of the kicked transverse Ising model. In the nonintegrable case we begin on extensive numerical studies that show that large multipartite entanglement is accompanied by diminishing two-body correlations, and that time averaged multipartite entanglement measures can be enhanced in nonintegrable systems.
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.
We investigate the entanglement arising naturally in a one-dimensional Ising chain in a magnetic field in an arbitrary direction. We find that for different temperatures, different orientations of the magnetic field give maximum entanglement. In the high-temperature limit, this optimal orientation corresponds to the magnetic field being perpendicular to the Ising orientation (z(z(z direction). In the low-temperature limit, we find that varying the angle of the magnetic field very slightly from the z direction leads to a rapid rise in entanglement. We also find that the orientation of the magnetic field for maximum entanglement varies with the field amplitude. Furthermore, we have derived a simple rule for the mixing of concurrences (a measure of entanglement) due to the mixing of pure states satisfying certain conditions.
An investigation of the entanglement and fidelity for two-qubit Ising model in an external uniform magnetic field showed that the entanglement degree oscillated with increasing phase decoherence in the initial stage and decreased with the increase in phase decoherence thereafter,the decline of the entanglement degree being greater with greater phase decoherence.When the initial state of the system was on its eigenstate,the concurrence was zero,or it did not change with the evolution of phase decoherence.The fidelity of the system exhibied an obvious periodic change and tended to remain at a constant value with the increase in phase decoherence.The entanglement degree and fidelity of the two-qubit Ising model could be enhanced or weakened through controlling magnetic field B.
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.