,Entanglement and quantum phase transition in alternating XY spin chain with next-nearest neighbouri

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By using the method of density-matrix renormalization-group to solve the different spin-spin correlation functions,the nearest-neighbouring entanglement (NNE) and the next-nearest-neighbouring entanglement (NNNE) of one-dimensional alteating Heisenberg XY spin chain are investigated in the presence of alteating the-nearestneighbouring interaction of exchange couplings,exteal magnetic fields and the next-nearest neighbouring interaction.For a dimerised ferromagnetic spin chain,the NNNE appears only above a critical dimerized interaction,meanwhile,the dimerized interaction a effects a quantum phase transition point and improves the NNNE to a large extent.We also study the effect of ferromagnetic or antiferromagnetic next-nearest neighbouring (NNN) interaction on the dynamics of NNE and NNNE.The ferromagnetic NNN interaction increases and shrinks the NNE below and above a critical frustrated interaction respectively,while the antiferromagnetic NNN interaction always reduces the NNE.The antiferromagnetic NNN interaction results in a large value of NNNE compared with the case where the NNN interaction is ferromagnetic.
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