【摘要】 应用键算符表象方法 ,在平均场近似下研究了自旋 1 /2量子 XY模型的基态性质 .模型建立在平面四方晶格上 ,形成纵列 dimer结构 .Dimer内两自旋之间的反铁磁相互作用为 J,dimer之间的反铁磁相互作用在 x方向和 y方向上分别为 J2 和 J1.给出了系统关于 J2 和 J1的无序—有序转变相图 ,计算了无序相下系统的基态能、自旋隙 ,以及 x方向和 y方向上的相干长度 .我们发现自旋隙出现在激发谱中的 ( 0 ,π)点 .一维 XY链 ( J2 =J,J1=0 )具有自旋隙 ,Δ=0 .1 65J,与利用自旋格林函数高阶退耦方法所得结果一致 .要消除这一自旋隙 ,链之间的耦合强度至少为 J1Cr=0 .0 43 J.一维链的相干长度为 3 .51 ,平均单自旋基态能为 -0 .3 2 1 J.一维 XY自旋梯 ( J1=J,J2 =0 )也同样具有自旋隙 ,Δ=0 .1 67J,比 Heisenberg自旋梯的自旋隙 0 .5J小 1,3 .当梯之间的人耦合强度达到 J1Cr=0 .0 61 J时 ,自旋隙消失 .自旋梯的相干长度为 5.97,平均单自旋基态能为 -0 .466J,比 Heisenberg自旋梯的平均单自旋基态能 -0 .578J大 1,3 .当 J2 =J1时 ,系统开始无自旋隙的临界值为 J1Cr=J2 Cr=0 .2 4J,比Heisenberg系统无自旋隙的临界值 0 .63 5J小更多还原

【Abstract】 The ground-state properties of spin-1/2 quantum XY model are studied by the bond-operator mean-field approach.The model is set on a square lattice with columnar dimer spin structure.The antiferromagnetic interaction is J between the two spins within a dimer,and are J 1 and J 2 in y and x directions between dimers,respectively.The diagram of disordered-ordered phase transition is given,and the ground-state energy,spin gap and correlation length are calculated in the disordered phase. It is found that the spin gap appears at the point(0,π) in the k space,the spin gap of Δ= 0.165J in the XY chain(J 2=J,J 1=0) is consistent with the value of 0.1J obtained by Green function theory with higher-order decoupling,and it is vanished at the critical value of J 1Cr=0.043J.The correlation length is 3.51,and the ground-state energy is -0.321Jper spin for the XY chain.The spin gap Δ of spin ladder(J 1=J,J 2=0) is 0.167J,smaller than the value of 0.5J in the Heisenberg model,and it is vanished at the critical value of J 2Cr=0.061J.The correlation length is 5.97 and the ground-state energy per spin is -0.466J,which is bigger than the value of -0.578J in the Heisenberg model.When J 2=J 1,the critical value of J 1Cr(=J 2Cr) for system having no spin gap is 0.24J,smaller than the value of 0.635J in the Heisenberg model.更多还原