Calculation of Pairwise Thermal Entanglement for Odd Qubit ⅩⅩ Chain

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Using Jordan-Winger transformation and finite Fourier transformation, the Hamiltonian of ⅩⅩ chain can be transformed to the diagonal form. If the total qubits number N = odd, the internal energy (U), and correlation function Gzz in thcrmal equilibrium can be calculated. Then the pairwise concurrence and the critical value βcr can be calculated.For N ≥ 5 ⅩⅩ chains, there are pairwise concurrences in thermal equilibrium for antiferromagnetic and ferromagnetic cases when β>βcr.
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