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arXiv:2009.07878

Entanglement robustness and spin relaxation in thermal states of two-dimensional dissipative spin system in an inhomogeneous magnetic field

Gehad Sadiek, Samaher Almalki

Published Sep 16, 2020• 0 citations
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Abstract

We consider a finite two-dimensional Heisenberg triangular spin lattice at different degrees of anisotropy coupled to a dissipative Lindblad environment obeying the Born-Markovian constrain at finite temperature. We show how applying an inhomogeneous magnetic field to the system may significantly affect the entanglement distribution and properties among the spins in the asymptotic steady state of the system. Particularly, applying an inhomogeneous field with an inward (growing) gradient toward the central spin is found to considerably enhance the nearest neighbor entanglement and its robustness to the thermal dissipative decay effect in the completely anisotropic (Ising) system, whereas all the beyond nearest neighbor entanglements vanish entirely. Applying the same field to a partially anisotropic (XYZ) system, does not only enhance the nearest neighbor entanglements and their robustness but also all the beyond nearest neighbor ones. Nevertheless, the inhomogeneity of the field shows no effect on the asymptotic behavior of the entanglement in the isotropic (XXX) system, which vanishes under any system configuration. Moreover, the same inhomogeneous field exhibits the most influential impact, compared with the other ones, on the the spin dynamics as well. Although in the isotropic system the spins relax to a separable (disentangled) steady state with all the spins reaching a common spin state regardless of the field inhomogeneity, the spins in the steady state of the completely anisotropic system reach different distinguished spin states depending on their positions in the lattice. However, in the XYZ system, though the anisotropy is lower, the spin states become even more distinguished, accompanying the long range quantum correlation across the system, which is a sign of a critical behavior taking place at this combination of system anisotropy and field inhomogeneity.

DOI
10.48550/arxiv.2009.07878

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We consider a finite two-dimensional Heisenberg triangular spin lattice at different degrees of anisotropy coupled to a dissipative Lindblad environment obeying the Born-Markovian constrain at finite temperature. We show how applying an inhomogeneous magnetic field to the system may significantly affect the entanglement distribution and properties among the spins in the asymptotic steady state of the system. Particularly, applying an inhomogeneous field with an inward (growing) gradient toward the central spin is found to considerably enhance the nearest neighbor entanglement and its robustness to the thermal dissipative decay effect in the completely anisotropic (Ising) system, whereas all the beyond nearest neighbor entanglements vanish entirely. Applying the same field to a partially anisotropic (XYZ) system, does not only enhance the nearest neighbor entanglements and their robustness but also all the beyond nearest neighbor ones. Nevertheless, the inhomogeneity of the field shows no effect on the asymptotic behavior of the entanglement in the isotropic (XXX) system, which vanishes under any system configuration. Moreover, the same inhomogeneous field exhibits the most influential impact, compared with the other ones, on the the spin dynamics as well. Although in the isotropic system the spins relax to a separable (disentangled) steady state with all the spins reaching a common spin state regardless of the field inhomogeneity, the spins in the steady state of the completely anisotropic system reach different distinguished spin states depending on their positions in the lattice. However, in the XYZ system, though the anisotropy is lower, the spin states become even more distinguished, accompanying the long range quantum correlation across the system, which is a sign of a critical behavior taking place at this combination of system anisotropy and field inhomogeneity.
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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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