Entanglement and quantum phase transition in alternating XY spin chain   with next-nearest neighbour interactions
  By using the method of density-matrix renormalization-group to solve the different spin-spin correlation functions, the nearest-neighbouring entanglement(NNE) and next-nearest-neighbouring entanglement(NNNE) of one-dimensional alternating Heisenberg XY spin chain is investigated in the presence of alternating nearest neighbour interactions of exchange couplings, external magnetic fields and next-nearest neighbouring interactions. For dimerized ferromagnetic spin chain, NNNE appears only above the critical dimerized interaction, meanwhile, the dimerized interaction effects quantum phase transition point and improves NNNE to a large value. We also study the effect of ferromagnetic or antiferromagnetic next-nearest neighboring (NNN) interactions on the dynamics of NNE and NNNE. The ferromagnetic NNN interaction increases and shrinks NNE below and above critical frustrated interaction respectively, while the antiferromagnetic NNN interaction always decreases NNE. The antiferromagnetic NNN interaction results to a larger value of NNNE in comparison to the case when the NNN interaction is ferromagnetic. 
C. J. Shan, W. W. Cheng, T. K. Liu, Y. X. Huang, H. Li