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)方晶格J1K模型的基态相图，目标(2)量子自旋向列相（QSN）的动力学特征，以及部分目标(3)关于确定QSN的微观性质。特别是，使用基于矩阵积态的方法，我不仅确定了QSN相，还确定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性相。在不相称的波矢量处发现了额外的不稳定性，导致QSN的动力学比先前预期的“幽灵”-Goldstone模式更丰富。可能的数值问题，即有限尺寸效应，已被调查，而不会导致更大的问题。与基塔耶夫磁体相关的第二个模型和类似于J1K模型的QSN阶段的键-四极矩也被研究了。主要区别在于，后者的对称性要低得多，四极矩是由于非对角线对称交换而自然发生的。尽管如此，在有效的一维模型中，已经发现了一种与托马纳加-卢廷格液体相关的量子自旋液体。预印本已经有了[arXiv:2212.11000]。我已经在会议和研讨会上以口头报告和海报形式展示了这两个项目的结果。第一份出版物目前正在准备中。

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.