Thermodynamics of frustrated spin lattices with flat bands

我们项目的中心目标是在尽可能大的晶格尺寸下对受挫量子自旋晶格的热力学性质进行评估和后续分析。我们相信这是一个独特的机会，因为我们可以在我们的团队中集合必要的先决条件：长期使用受挫的量子自旋晶格的经验，长期使用有限温度Lanczos方法(FTLM)的经验，以及最后但同样重要的是直接访问代码SPINPACK。此代码使我们能够在莱布尼茨超级计算中心(LRZ)Garching使用新的超级计算机SuperMUC-ng，最大节点数为3076，即147,648个核心。我们属于那些在公开使用之前被授予访问权限的用户，以便测试机器。特别是，我们想要研究尺寸为N=45和N=48的Kagome晶格海森堡反铁磁体(KHAF)在1/3磁化平台的热力学性质，以解释不对称熔化现象。我们将研究与温度和场相关的磁化强度以及态密度。对于N=81的晶格尺寸，我们想要研究KHAF上的磁振子结晶，对于这种情况，首先研究在饱和场以下，即在7/9磁化平台，强烈地指向与二维三态Potts模型相同普适类的相变。日本研究小组建议的其他磁化高原的磁振子凝聚也应进行调查。我们确信他们来自不同的起源。我们的研究将通过对同样具有平带的相关受挫自旋系统的类似研究来完成，特别是方形Kagome晶格和平面焦绿石晶格。尤其是正方形的Kagome晶格是一个亟待解决的问题，因为这种结构可以在很近的时间内合成出来，而且第一次实验也发表了。在项目持续时间的最后三分之一，我们希望从海森堡模型转向XXZ耦合以及次近邻耦合，以便调整系统的挫折度以及使平坦的频带变形。这不仅涉及现实的化合物，而且还应该有助于理解特定挫折效应对例如磁热特性的影响。另一个问题是研究自旋量子数对寻址性质的影响。除了比较各种晶格之外，整个项目中的J1-J2正方形晶格将作为具有可调挫折度的参照系。此外，热力学函数将与基于高温级数展开和所谓的熵方法相结合的插值法进行比较。

The central goal of our project is the evaluation and subsequentanalysis of thermodynamic properties of frustrated quantum spin lattices for as big lattice sizes as possible. We are convinced that this is a unique opportunity since we could assemble the neccessary prerequisites in our team: long experience with frustrated quantum spin lattices, long experience with the finite-temperature Lanczos method (FTLM,) and last but not least direct access to the code spinpack. This code enables us to use the new supercomputer supermuc-ng at the Leibniz Supercomputing Center (LRZ) Garching with up to the Maximum number of nodes, 3076, i.e. 147,648 cores. We belong to those users who were given access prior to public use in order to test the machine. In particular, we want to investigate thermodynamic properties of the kagome lattice Heisenberg antiferromagnet (KHAF) for sizes N=45 and N=48 at the 1/3rd magnetization plateau in order to elucidate the phenomenon of asymmetric melting. Temperature and field dependent magnetization as well as the density of states will be studied. For lattice sizes of up to N=81 we want to study magnon crystallization on the KHAF, for which first investigations below the saturation field, i.e. at the 7/9 magnetization plateau, strongly point at a phase transition of the sameuniversality class as the two-dimensional 3-states Potts model. The magnon condensation suggested by a Japanese team for other magnetization plateaus, shall be investigated as well. We are convinced that they are of different origin. Our investigations shall be completed by similar studies for related frustrated spin systems that also possess flat bands, in particular the square kagome lattice and the planar pyrochlore lattice. Especially the square kagome lattice turned out to be an urgent problem since this structure could be synthesized quite recently and first experiments were published. During the last third of the project duration we would like to move away from a Heisenberg model towards XXZ couplings as well as next-nearest neighbor couplings in order to tune the frustration of the system as well as to deform the flat bands. This not only addresses realistic compounds, but should also help to understand the impact of specific frustration effects on e.g. magnetocaloric properties. Another issue along this line is the investigation how the spin quantum number influences the addressed properties.Besides comparing the various lattices, the J1-J2 square lattice throughout theproject will serve as reference system with tunable frustration. In addition, thermodynamic functions will be compared with an interpolation method that rests on high-temperature series expansions combined with a so-called entropy method.