Abstract

In 1983, F. Duncan M. Haldane predicted a singlet ground state for isolated integer-spin one-dimensional antiferromagnets with low single-ion anisotropy D. Since then, a lot of species containing chains of integer spin ions were tested to check the basic conjecture on an energy gap separating the continuum of the excited states from the ground state. As a result of these studies, it has been established that there are numerous states competing with the Haldane phase, namely long-range ordered, dimerized, and large-D phases. The long-range magnetic order takes place due to sufficiently strong exchange interactions between adjacent chains. Dimerization results from the alternation of the exchange interactions within the chains. Both uniaxial and rhombic single-ion anisotropies can suppress the Haldane phase, which is robust only until some critical values. The choice between the competing phases depends also on exchange anisotropy. Excellent reviews on the basic results obtained during the first 20 years of investigation of these phenomena provided solid background for the future studies. Here, we present some developments in this field obtained over the next two decades of research on spin-1 chain systems.

摘要

1983 年，F. Duncan M. Haldane 预测了具有低单离子各向异性D 的孤立整数自旋一维反铁磁体的单线态基态。从那时起，测试了许多包含整数自旋离子链的物质，以检查关于将激发态的连续谱与基态分开的能隙的基本猜想。作为这些研究的结果，已经确定有许多状态与 Haldane 相竞争，即长程有序、二聚和大D阶段。由于相邻链之间足够强的交换相互作用，发生长程磁序。二聚化源于链内交换相互作用的交替。单轴和菱形单离子各向异性都可以抑制霍尔丹相，它仅在某些临界值之前是稳健的。竞争相之间的选择还取决于交换各向异性。在对这些现象的前 20 年调查中获得的基本结果的优秀评论为未来的研究提供了坚实的背景。在这里，我们介绍了在接下来的二十年对 spin-1 链系统的研究中获得的该领域的一些进展。