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 solve the different spin spin correlation functions, the nearest-neighbouring entanglement （NNE） and the next-nearest-neighbouring entanglement （NNNE） of one-dimensional alternating Heisenberg XY spin chain are investigated in the presence of alternating the-nearestneighbouring interaction of exchange couplings, external 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.

Alternating Double Trinucleate[Yb_3(μ_3-OH)_2O]_2 Chain Bridged byμ_3-OH Mode in a 3D Yb^(3+)-CP and Its Near Infrared Luminescent Properties

A new 3D coordination polymer,namely,[Yb_3（μ_3-OH）_3（μ_2-OH）（DDLA）_（2.5）（BIPY）]（1,H_2DDLA = 2,2-dipyridyl-4,4-dicarboxylic acid,BIPY = 2,2？-bipyridine）,has been synthesized via solvothermal method. The complex crystallizes in triclinic,space group P1 with a = 7.7339（4）,b = 15.6699（8）,c = 17.2221（9） ？,α = 68.8630（10）,β = 88.1890（10）,γ = 88.1740（10）°,V = 1945.27（17） ？~3,Z = 2,D_c = 2.296 g·cm^3,μ（MoKα） = 1.075 mm^（-1）,F（000） = 1268,S = 1.068,R = 0.0263 and wR = 1.067 for 5176 observed reflections with I 〉 2σ（I）. Compound 1 contains a unique alternating double trinucleate {[Yb_3（μ_3-OH）_2OH]_2}_n chain,in which Yb^（3＋） is bridged through μ_3-OH and μ_2-OH two coordination modes. The alternating double trinucleate chains are further extended into a 3D structure through DDLA^（2-） ligands by different coordination modes. The photoluminescence spectra show 1 is highly sensitized by the characteristic emission of Yb^（3＋） in the NIR region.

A Novel Copper(II) Coordination Polymer with Figure-of-eight-shaped Channels Occupied by Flexible Monodentate and Bidentate N,N′-bipyrdyl Ligands

A copper（Ⅱ） coordination polymer, [Cu3（HOA）2（bpp）4]n （1, HnOA = 3,3＇,4,4＇- oxidiphthalic acid, bpp = 1,3-bis（4-pyridyl） propane）, has been hydrothermally synthesized. The crystal structure is of monoclinic, space group P21/c with a = 11.544（3）, b = 16.129（4）, c = 21.181 （6） A, β = 98.848（5）, V= 3897.0（2） A3, C84018N8H70Cu3, Mr = 1670.13, Z = 2, De = 1.423 g/cm^3, F（000） = 1722, μ = 0.887 mm^-1, R = 0.0878 and wR = 0.2583 for 8496 observed reflections （I 〉 2σ（I））. Single-crystal X-ray structural analysis reveals that 1 is a three-dimensional （3D） framework based on a two-dimensional （2D） mesomeric layer of alternating left- and fight-handed helical chains. The monodentate terminal and bidentate bridging bpp ligands in the same conformation are all encapsulated in the figure-of-eight-shaped channels, thus further stabilizing the whole three-dimensional framework.

Analytical and Numerical Studies of Quantum Plateau State in One Alternating Heisenberg Chain

By using the coupled duster method and the numerical density matrix renormalization group method, we investigate the properties of the quantum plateau state in an alternating Heisenberg spin chain. In the absence of a magnetic field, the results obtained from the coupled cluster method and density matrix renormalization group method both show that the ground state of the aiternating chain is a gapped dimerized state when the parameter a exceeds a critical point ac. The value of the critical points can be determined precisely by a detailed investigation of the behavior of the spin gap. The system therefore possesses an m = 0 plateau state in the presence of a magnetic field When a 〉 ac. In addition to the m = 0 plateau state, the results of density matrix renormaiization group indicate that there is an m = 1/4 plateau state that occurs between two critical fields in the alternating chain if a 〉 1. The mechanism for the m = 1/4 plateau state and the critical behavior of the magnetization as one approaches this plateau state are also discussed.