Numerical Study of Quantum Spin-Nematic Order in Frustrated Ferromagnets and its Relation to Quantum Spin Liquids

关于我的建议，我主要完成了目标（1）正方格子J1 K模型的基态相图，目标（2）量子自旋共振（QSN）相的动力学特征，以及部分目标（3）关于识别QSN的微观性质。特别是，使用基于矩阵乘积态的方法，我不仅识别了QSN相，而且是四亚晶格偶极有序态、强烈倾斜的两亚晶格反铁磁体和矢量手征相。一个额外的不稳定性被确定在无公度波矢量导致更丰富的动力学QSN比以前预期的'鬼'-Goldstone模式。可能的数值问题，即有限尺寸的影响，已被调查，没有导致更大的问题。第二个模型相关Kitaev磁铁和托管键四极矩类似的QSN相位的J1 K模型进行了研究。主要区别在于，后者确实具有低得多的对称性，并且由于非对角对称交换而自然发生四极矩。尽管如此，一个量子自旋液体相关的Tomanaga-Luttinger液体在一个有效的1D模型已经被发现。一个预印本已经可用[arXiv：2212.11000]。我已经提出了两个项目的结果作为口头报告，并在会议和研讨会上作为海报介绍。目前正在编写第一份出版物。

With respect to my proposal, I have mostly finished goal (1) the ground state phase diagram of the square-lattice J1K model, goal (2) dynamical signatures of the quantum spin-nematic (QSN) phase, and partly goal (3) about identifying the microscopic nature of the QSN.In particular, using matrix product state based methods, I have identified not only the QSN phase, but also a four-sublattice dipolar ordered state, a strongly canted two-sublattice antiferromagnet, and a vector-chiral phase. An additional instability was identified at incommensurate wave vectors resulting in richer dynamics of the QSN than the previously anticipated 'ghost'-Goldstone mode.Possible numerical issues, i.e. finite-size effects, have been investigated not resulting in bigger issues.A second model related to Kitaev-Magnets and hosting bond-quadrupole moments similar to the QSN phase of the J1K model was studied as well. The main difference being, that the latter does have much lower symmetry and quadrupole moments are naturally occurring due to off-diagonal symmetric exchange. Nonetheless, a quantum spin liquid related to a Tomanaga-Luttinger liquid in an effective 1D model has been found. A preprint is already available [arXiv:2212.11000].I have presented results of both projects as oral presentations and as a poster presentations at conferences and as seminars. A first publication is currently in preparation.