Entanglement and quantum phase transition in alternating XY spin chain with next-nearest neighbouring interactions

By using the method of density-matrix renormalization-group to solvethe different spin--spin correlation functions, thenearest-neighbouring entanglement (NNE) and thenext-nearest-neighbouring entanglement (NNNE) of one-dimensionalalternating Heisenberg XY spin chain are investigated in thepresence of alternating the-nearest-neighbouring interaction ofexchange couplings, external magnetic fields and the next-nearestneighbouring interaction. For a dimerised ferromagnetic spin chain,the NNNE appears only above a critical dimerized interaction,meanwhile, the dimerized interaction a effects a quantum phasetransition point and improves the NNNE to a large extent. We alsostudy the effect of ferromagnetic or antiferromagnetic next-nearestneighbouring (NNN) interaction on the dynamics of NNE and NNNE. Theferromagnetic NNN interaction increases and shrinks the NNE belowand above a critical frustrated interaction respectively, while theantiferromagnetic NNN interaction always reduces the NNE. Theantiferromagnetic NNN interaction results in a large value of NNNEcompared with the case where the NNN interaction is ferromagnetic.