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

关于我的提议，我已经基本完成了目标(1)正方形晶格J1K模型的基态相图，目标(2)量子自旋向列(QSN)相的动力学特征，以及部分目标(3)关于识别QSN相的微观性质。特别是，利用基于矩阵积的方法，我不仅识别了QSN相，而且还识别了四亚晶格偶极有序态、强倾斜的两亚晶格反铁磁体和矢量手征相。在非公度波矢上发现了一个额外的不稳定性，导致QSN的动力学比先前预期的‘幽灵’-Goldstone模型更丰富。可能的数值问题，即有限尺寸效应，已经被研究过，但没有导致更大的问题。第二个模型与Kitaev磁体有关，并拥有类似于J1K模型的QSN相的键-四极矩。主要的区别是，后者的对称性确实要低得多，四极矩是由于非对角线对称交换而自然产生的。然而，在一个有效的一维模型中，已经发现了与Tomanaga-Luttinger液体相关的量子自旋液体。已有预印本[arxiv：2212.11000]，我已将这两个项目的成果作为口头陈述和在会议和研讨会上的海报陈述。第一份出版物目前正在筹备中。

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.