Abstract
The differences between the XXZ model with topological and periodical boundary conditions were compared by studying their entanglement, quantum discord, and critical temperature above which the entanglement vanishes. It shows that the different boundary conditions mainly affect bipartite quantum correlations of the boundary spins rather than that of other spin pairs. The topological boundary spins can protect entanglement and discord against strong magnetic fields while the periodical boundary spins can protect them against nonuniform magnetic fields. Compared with the periodical XXZ model, the critical temperature is significantly improved for the topological XXZ model. The topological XXZ model also allows us to improve significantly its critical temperature by increasing the strength of magnetic field, which is not feasible for the periodical XXZ model. It is therefore more promising for preparing entangled states at high temperature in the topological XXZ model.
Highlights
Integrable models provide exact solutions for understanding some non-trivial physical phenomena in statistical physics, quantum field theory and condensed matter physics[1,2,3,4]
The differences between quantum correlations in the XXZ model with periodical and topological conditions are compared in detail, through which it was found that the topological boundary condition is beneficial for the protection of entanglement against thermal fluctuations in the considered model
The three-qubit XXZ model with periodical and topological boundary conditions have been investigated by calculating their bipartite entanglement, bipartite discord, tripartite entanglement, and corresponding critical temperature
Summary
The boundary spins of the XXZ model with topological boundary condition possess bipartite entanglement even with B = 0, while this is not the case for that with the periodical boundary condition. There are two triangular regions representing strong magnetic fields B where the negativity vanishes for the case of periodical boundary condition while exists for the case of topological boundary condition It means that the tripartite entanglement can exist in the region of strong magnetic field for the topological XXZ model. In addition to a nonuniform magnetic field, the topological boundary condition allows us to improve Tc for the XXZ model via another approach, i.e., increasing the strength of magnetic field B There is another interesting phenomenon that Tc of tripartite entanglement is higher than Tc of bipartite entanglement in periodical XXZ model. For the periodical XXZ model, there is a region in which the existence of tripartite entanglement is a necessary condition for existence of bipartite entanglement
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