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Thermal entanglement properties of N-qubit quantum Heisenberg chain in a two-component magnetic field

We elucidate the finite temperature entanglement properties of $N=9$ qubits Heisenberg $XX$ and $XXZ$ models under the presence of a polarized magnetic field in $xz$ plane by means of concurrence concept. We perform a systematic analysis for a wide range of the system parameters. Our results suggest that the global phase regions which separate the entangled and non-entangled regions sensitively depend upon the spin-spin interaction term of the $z-$ component of two neighboring spins $J_{z}/J_{x}$, temperature as well as polarized magnetic field components. Thereby, we think that polarized magnetic field can be used a control parameter to determine the amount of thermal entanglement between pair of qubits for different temperatures and spin-spin interaction terms. Moreover, it has been found that the nearest-neighbor pair of qubits does not point out a re-entrant type entanglement character when one only deals with the nearest-neighbor pair of qubits. However, as one considers next-nearest neighbor pair of qubits, it is possible to see the evidences of re-entrant type entanglement behaviors.