Tensor Network Approach for the Two-Dimensional Kondo Lattice

二维近藤晶格的张量网络方法

• 批准号: 439706636
• 负责人: Dr. Matthias Peschke
• 金额: --
• 依托单位: Faculteit der Natuurwetenschappen, Wiskunde en Informatica
• 依托单位国家: 德国
• 项目类别: Research Fellowships
• 财政年份: 2020
• 资助国家: 德国
• 起止时间: 2019-12-31 至 无数据
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/439706636?language=en
• 关键词: Tensor; Network; Approach; Two; Dimensional

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.

二维强相关电子系统是凝聚态物质理论中最有趣的一类。在这里，强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、电荷的集体顺序和轨道自由度。当晶格的几何形状与磁序不相容时，奇异磁相就会出现。这种效应在技术语言中被称为几何挫折。本研究项目的目的是研究几何挫折晶格结构上具有电子和磁性自由度的二维系统的磁性。为此，本文将采用一种最新的张量网络分析方法（无限投影纠缠对状态（iPEPS）方法）对系统进行数值模拟。因此，可以精确地结合粒子之间的相互作用。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介质。因此，几何挫折的结合可以在电子系统上产生有趣的反馈。计算将对三角形晶格以及具有额外对角线连接的方形晶格进行。这两种晶格结构都与反铁磁秩序不相容，因此代表了受挫系统。所得的结果将然后结合起来，以获得对几何挫折对磁性的影响的一般理解。所使用的模型是近藤晶格，是为定性描述重费米子系统的磁性而设计的。对这类材料已有的实验表明，底层晶格在几何上受挫的化合物确实具有奇异的磁性状态。化合物CePdAl就是一个具体的例子。目前的研究项目应该有助于理解这些奇异相的定性机制。