Quantum correlations and entanglement in a Kitaev-type spin chain
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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. But peculiarly in this model, the entanglement measures do not show any singular behavior in the vicinity of the critical point, as seen in the transverse Ising model ground state and related models. We have investigated different correlation measures analytically, that have been used for many solvable spin systems to track a quantum critical point. We compute the pair concurrence measure of entanglement, the pair quantum discord to track the quantum correlations, and a global entanglement measure and a multi-species entanglement measure to investigate multi-party 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 multi-species entanglement shows the most-pronounced signature of the critical point, in its first-order derivative, though the entanglement and its derivatives have a smooth behavior in the critical region.
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