Institut für Theoretische Physik, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany.
J Phys Condens Matter. 2010 Nov 10;22(44):446002. doi: 10.1088/0953-8984/22/44/446002. Epub 2010 Oct 22.
We use the coupled cluster method for infinite chains complemented by exact diagonalization of finite periodic chains to discuss the influence of a third-neighbor exchange J(3) on the ground state of the spin-½ Heisenberg chain with ferromagnetic nearest-neighbor interaction J(1) and frustrating antiferromagnetic next-nearest-neighbor interaction J(2). A third-neighbor exchange J(3) might be relevant to describe the magnetic properties of the quasi-one-dimensional edge-shared cuprates, such as LiVCuO(4) or LiCu(2)O(2). In particular, we calculate the critical point J(2)(c) as a function of J(3), where the ferromagnetic ground state gives way for a ground state with incommensurate spiral correlations. For antiferromagnetic J(3) the ferro-spiral transition is always continuous and the critical values J(2)(c) of the classical and the quantum model coincide. On the other hand, for ferromagnetic J3 is < or approximately equal to -(0.01...0.02)|J1|. the critical value J(2)(c) of the quantum model is smaller than that of the classical model. Moreover, the transition becomes discontinuous, i.e. the model exhibits a quantum tricritical point. We also calculate the height of the jump of the spiral pitch angle at the discontinuous ferro-spiral transition.
我们使用无限链的耦合簇方法，并通过有限周期链的精确对角化来讨论第三近邻交换 J(3) 对具有铁磁近邻相互作用 J(1) 和反铁磁次近邻相互作用 J(2) 的自旋-½ 海森堡链基态的影响。第三近邻交换 J(3) 可能与描述准一维共享边缘的铜酸盐的磁性质有关，例如 LiVCuO(4) 或 LiCu(2)O(2)。特别是，我们计算了作为 J(3) 函数的临界点 J(2)(c)，其中铁磁基态让位于具有非共调螺旋相关的基态。对于反铁磁 J(3)，铁-螺旋转变总是连续的，经典模型和量子模型的临界值 J(2)(c) 是一致的。另一方面，对于铁磁 J3<或近似等于-(0.01...0.02)|J1|，量子模型的临界点 J(2)(c)小于经典模型的临界点 J(2)(c)。此外，转变变得不连续，即模型表现出量子三临界点。我们还计算了不连续铁-螺旋转变时螺旋螺距角跳跃的高度。
