Tensor Network Approach for the Two-Dimensional Kondo Lattice

二维强关联电子系统是凝聚态理论中最有趣的一类。在这里，强大的量子效应导致物质的迷人状态，例如非费米液体行为，高温超导性和电荷的集体秩序和轨道自由度。特别是当晶格的几何形状与磁序不相容时，会出现奇异的磁相。本研究的目的是研究二维系统的磁特性，电子和磁自由度的几何挫格结构。为此，最近的张量网络的ananimals（无限投射纠缠对态（iPEPS）的方法）将被应用到模拟系统的数值。因此，可以精确地结合颗粒之间的相互作用。这种系统的磁性特别有趣，因为电子部分充当不同磁性成分之间的媒介。因此，几何挫折的结合可以导致对电子系统的有趣的反馈。将对三角形晶格以及具有附加对角链接的正方形晶格执行计算。这两种晶格结构与反铁磁序不相容，因此代表了受抑系统。所得到的结果将被结合起来，以获得一个几何挫折的影响magnetics.The所使用的模型是近藤晶格和设计的定性描述的重费米子系统的磁性的一般理解。已经存在的实验表明，这类材料确实异国情调的磁性状态的化合物，其中的基础晶格是几何挫折。化合物CePdAl代表一个具体的例子。目前的研究项目应有助于了解这些外来相的定性机制。

Two-dimensional strongly correlated electron systems are one of the most interesting classes of condensed matter theory. Here, strong quantum effects lead to fascinating states of matter such as for example non-Fermi liquid behavior, high-temperature superconductivity and collective order of charge and orbital degrees of freedom. Exotic magnetic phases appears especially if the geometry of the lattice is not compatible with the magnetic order. This effect is called geometrical frustration in technical language.The aim of the present research project is to investigate the magnetic properties of two-dimensional systems with electronic and magnetic degrees of freedom on geometrically frustrated lattice structures. To this end, a recent tensor network ansatz (the infinite projected entangled pair state (iPEPS) approach) will be applied to simulate the system numerically. Thereby, it is possible to incorporate the interactions between the particles accurately. The magnetism of such systems is in particular interesting because the electronic part acts as the mediator between the different magnetic constituents. The incorporation of geometrical frustration can thus lead to an interesting feedback on the electronic system. The computations will be performed for the triangular lattice as well as for a square lattice with additional diagonal links. Both lattice structures are not compatible with antiferromagnetic order and represent therefore frustrated systems. The obtained results will then be combined to gain a general understanding of the impact of geometrical frustration on the magnetism.The used model is the Kondo lattice and is designed for the qualitative description of the magnetic properties of heavy-fermion systems. Already existing experiments for these class of materials show indeed exotic magnetic states for compounds in which the underlying lattice is geometrically frustrated. The compound CePdAl represents a concrete example. The present research project should help to understand the qualitative mechanism for these exotic phases.