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Journal of Physics Conference Series

Impurity effect on entanglement asymptotic state in one-dimensional Ising system coupled to a dissipative environment

Gehad Sadiek

Published Jul 1, 2017• 1 citation
Publisher

Abstract

We consider a finite one-dimensional Ising spin chain under the influence of a dissipative Lindblad environment obeying the Born-Markovian constrain in presence of an external magnetic field with open boundary conditions. We study the effect of a single impurity, located at the terminal or center of the chain, on the time evolution and asymptotic steady state of the bipartite entanglement in the chain starting from a maximally entangled initial state. We found that the impurity has a significant effect on the bipartite entanglement of its nearest spins and can be used to tune their steady state value but has almost no noticeable impact on the far ones. At finite temperature, the thermal excitations suppress the dynamics of the system and reduce the value of the steady state and may completely wipe it out as the temperature is increased, which eliminates the effect of the impurity in that case.

DOI
10.1088/1742-6596/869/1/012022

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We consider a finite one-dimensional Ising spin chain under the influence of a dissipative Lindblad environment obeying the Born-Markovian constrain in presence of an external magnetic field with open boundary conditions. We study the effect of a single impurity, located at the terminal or center of the chain, on the time evolution and asymptotic steady state of the bipartite entanglement in the chain starting from a maximally entangled initial state. We found that the impurity has a significant effect on the bipartite entanglement of its nearest spins and can be used to tune their steady state value but has almost no noticeable impact on the far ones. At finite temperature, the thermal excitations suppress the dynamics of the system and reduce the value of the steady state and may completely wipe it out as the temperature is increased, which eliminates the effect of the impurity in that case.
We consider a finite one-dimensional Heisenberg XYZ\mathit{XYZ}XYZ spin chain under the influence of a dissipative Lindblad environment obeying the Born-Markovian constraint in presence of an external magnetic field with closed and open boundary conditions. We present an exact numerical solution for the Lindblad master equation of the system in the Liouville space. The dynamics and asymptotic behavior of the nearest-neighbor and beyond-nearest-neighbor pairwise entanglements in the system are investigated under the effect of spatial anisotropy, temperature, system size, and different initial states. The entanglements in the free spin system exhibit nonuniform oscillatory behavior that varies significantly depending on the system size, anisotropy, and initial state. The xyxyxy spatial anisotropy dictates the asymptotic behavior of the different entanglements in the system under the influence of the environment regardless of the initial state. Higher anisotropy yields higher steady-state value of the nearest-neighbor entanglement whereas a complete isotropy wipes it out. The longer range entanglements respond differently to the anisotropy variation. The anisotropy in the zzz direction may enhance the entanglements depending on the interplay with the magnetic field applied in the same direction. As the temperature is raised, the steady state of the short-range entanglements is found to be robust within very small nonzero temperature range that depends critically on the spatial anisotropy. Moreover, the end to end entanglement transfer time and speed through the open boundary chain vary considerably based on the degree of anisotropy and temperature of the environment.
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Abstract Many of the recently developed quantum systems that are considered promising candidates for the underlying technology of quantum computing enjoy long-range interaction, which is even tunable in some of them. Most of these systems can be described using the Heisenberg spin model to represent their interaction with the same system or a different one in hybrid structures. We consider here a finite two-dimensional spin system with a varying spin-spin long-range interaction under the effect of an external uniform magnetic field. We investigate the dynamics of the system and its asymptotic behavior at different degrees of anisotropy and interaction range under coupling to a thermal dissipative environment, starting from different initial states. We show that the system spin state and bipartite entanglement evolve in time to reach asymptotic values that are enhanced significantly by the degree of anisotropy and interaction range, whereas the thermal dissipative environment degrades the entanglement asymptotic equilibrium value as the temperature increases. Interestingly, while the robustness of the spin system against the environment’s thermal dissipative effects increases with the interaction range and degree of anisotropy, the entanglement between the far sites on the lattice shows its highest resilience in the partially anisotropic system, which might be attributed to a critical behavior taking place in the system. While the system’s early dynamics varies significantly depending on the initial state, the asymptotic equilibrium value is found to be completely independent.
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