Critical behaviour of collective excitations as a probe for exotic quantum phases - Bound states in a bilayer of Heisenberg models on the kagome lattice

对具有拓扑量子序的奇异相的研究是现代物理学中最有趣和最吸引人的课题之一。这种带隙的量子相位是高度纠缠的状态，其中基本性质如基态的数量取决于拓扑的属。此外，这些相位具有高度奇异的基本激发，即所谓的任意子，其粒子统计不同于费米子和玻色子。因此，拓扑有序的量子系统是基础科学的基本兴趣。此外，这些相位是拓扑量子计算的相关对象。在这里，量子信息是在这些系统的拓扑性质中存储和处理的，这样就可以对局部退相干进行拓扑保护，这是这个概念与量子信息中的其他方法相比的核心优势。因此，识别具有拓扑量子秩序的现实模型具有重要意义。为此，几何挫折可能是一个关键的旋钮，以破坏其他传统有序的物质状态。研究截头量子系统的圣杯是二维Kagome格点上的海森堡模型。经过几十年的深入研究，最近的数值结果表明，拓扑有序的自旋带隙液体基态。本计画的中心思想是研究两个可果美平面在横向上以一个无阻挫的海森堡耦合来耦合。在这个项目中提出的基本问题是，人们是否可以理解的性质和性质的奇异拓扑秩序的Kagome海森堡模型通过研究大的横向耦合的平凡相的崩溃，其中一个发现占主导地位的单线态的横向二聚体。人们可能会认为相变可以描述为两粒子束缚态的凝聚，总自旋为零。因此，我们想计算单粒子和双粒子激发能作为高阶级数展开的价键晶体相存在于大的横向耦合。这应该允许获得一个更好的理解外来相由于常规阶段的临界击穿的调查在一个非常一般的水平。

The investigation of exotic phases with topological quantum order represents one of the most interesting and fascinating topics in modern physics. Such gapped quantum phases are highly entangled states where elementary properties like the number of ground states depends on the genus of the topology. Furthermore, such phases have highly exotic elementary excitations, so-called anyons, having a particle statistic different from fermions and bosons. Topologically ordered quantum systems are therefore of fundamental interest for basic science. Furthermore, such phases are the relevant objects for topological quantum computation. Here quantum information is stored and processed in the topological properties of these systems such that one has a topological protection against local decoherence which is the central advantage of this concept compared to other approaches in quantum information.It is therefore of big relevance to identify realistic models having topological quantum order. To this end geometrical frustration is likely a key knob in order to destabilize other conventionally ordered states of matter. The holy gral in the research on frustated quantum systems is the Heisenberg model on the two-dimensional Kagome lattice. After decades of intensive research recent numerical results indicates a topologically ordered gapped spin liquid ground state. It is the central idea of this project to study two kagome planes which are coupled with an unfrustrated Heisenberg coupling in the transverse direction. The fundamental question asked in this project is whether one can understand the nature and the properties of the exotic topological order in the Kagome Heisenberg model by studying the breakdown of the trivial phase at large transverse couplings where one finds dominantly singlets on the transverse dimers. One then might expect that the phase transition can be described as the condensation of two-particle bound states with total spin zero. We therefore would like to calculate single and two-particle excitations energies as high-order series expansions out of the valence bond crystal phase present at large transverse couplings. This should allow to gain an improved understanding of exotic phases due to the investigation of the critical breakdown of conventional phases on a very general level.