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

集体激发作为奇异量子相探针的临界行为 - kagome 晶格上海森堡模型双层中的束缚态

基本信息

批准号：
261850484
负责人：
Professor Dr. Kai Phillip Schmidt
金额：
--
依托单位：
Lehrstuhl für Statistische Physik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2014
资助国家：
德国
起止时间：
2013-12-31 至 2015-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/261850484?language=en
关键词：
Critical behaviour collective excitations probe

项目摘要

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.

对具有拓扑量子秩序的奇异相的研究是现代物理学中最有趣和最迷人的话题之一。这种缺口量子相是高度纠缠态，其中基本性质，如基态的数量取决于拓扑的属。此外，这些相具有高度奇异的基本激发，即所谓的任意子，具有与费米子和玻色子不同的粒子统计量。因此，拓扑有序量子系统对基础科学具有重要意义。此外，这些相位是拓扑量子计算的相关对象。在这里，量子信息在这些系统的拓扑特性中被存储和处理，这样就有一个拓扑保护来防止局部退相干，这是与量子信息中的其他方法相比，这个概念的核心优势。因此，识别具有拓扑量子秩序的现实模型具有重要意义。为了达到这个目的，几何挫折感可能是一个关键的旋钮，以破坏物质的其他传统有序状态。二维Kagome晶格上的海森堡模型是研究受挫量子系统的圣杯。经过几十年的深入研究，最近的数值结果表明了一种拓扑有序的间隙自旋液体基态。这个项目的中心思想是研究两个kagome平面，它们在横向上与海森堡耦合耦合。在这个项目中提出的基本问题是，人们是否可以通过研究在横向二聚体上主要发现单线态的大横向耦合中的平凡相的击穿来理解Kagome Heisenberg模型中奇异拓扑秩序的性质和性质。因此，人们可能期望相变可以被描述为总自旋为零的两粒子束缚态的凝聚。因此，我们希望计算出在大型横向耦合中价键晶体相外的高阶级数展开时的单粒子和双粒子激发能。由于在非常普遍的水平上对常规相的临界击穿进行了研究，这将使我们对奇异相有了更好的理解。