EAPSI: Investigating the Stability of Particles in Topological Phases of Matter

EAPSI：研究物质拓扑相中粒子的稳定性

• 批准号: 1515557
• 负责人: Matthew Cha
• 金额: $ 0.01万
• 依托单位: Cha Matthew
• 依托单位国家: 美国
• 项目类别: Fellowship Award
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-06-01 至 2016-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1515557&HistoricalAwards=false
• 关键词: EAPSI; Investigating; Stability; Particles; Topological

A fundamental challenge in science is to characterize states of matter. A phase of matter is a family of states of matter which have very uniform physical properties. Common phases include liquid, gas and solid, which are distinguished by varying temperature. In the 1980?s, scientist discovered new phases of matter in two dimensional electron gas structures, namely fractional quantum hall states. These states possessed particles with interesting statistical behavior, called anyons. In particular, an exchange of two anyons resulted in a multiplication of the state by a complex phase. These new states of matter belong to topologically ordered phases. This project investigates the conjecture that the structure of anyons is stable within a topological phase. This research will be conducted in collaboration with Dr. Yasuyuki Kawahigashi, professor in the Department of Mathematical Science at the University of Tokyo. Dr. Kawahigashi is an expert in the theory of operator algebras and their applications to mathematical physics. The collaboration allows us to further explore the operator algebraic perspective of topological phases and pursue rigorous results in the subject. This research will advance efforts to realize universal quantum computing.We begin by studying exactly solvable Hamiltonian lattice models, in the thermodynamic limit, for which the anyon structure is completely known. These models include Kitaev?s surface codes and Levin and Wen?s string-net models. Each anyon is related to a superselection sector of the algebra of observables. Analysis of the superselection sectors allows one to recover the complete anyon structure, including particle fusion and braiding. Under physically allowable perturbations, we will study the stability of the superselection sectors and particle fusion and braiding. The stability of anyons is the premise of a major program in fault-tolerant quantum computation, namely topological quantum computation. The results of this project form the basis for the continued search for a universal quantum computer through topologically ordered states. This NSF EAPSI award is funded in collaboration with the Japan Society for the Promotion of Science.

科学的一个基本挑战是表征物质的状态。 物质相是具有非常一致的物理性质的物质状态族。 常见的相包括液体、气体和固体，它们通过不同的温度来区分。 20 世纪 80 年代，科学家在二维电子气结构中发现了新的物质相，即分数量子霍尔态。 这些态拥有具有有趣统计行为的粒子，称为任意子。 特别是，两个任意子的交换导致状态乘以复相。 这些新的物质状态属于拓扑有序相。 该项目研究了任意子结构在拓扑相内稳定的猜想。 这项研究将与东京大学数学科学系教授 Yasuyuki Kawahigashi 博士合作进行。 Kawahigashi 博士是算子代数理论及其在数学物理中的应用方面的专家。 此次合作使我们能够进一步探索拓扑相的算子代数视角，并在该主题中追求严格的结果。 这项研究将推进实现通用量子计算的努力。我们首先研究在热力学极限下精确可解的哈密顿晶格模型，其中任意子结构是完全已知的。 这些模型包括 Kitaev 的表面编码以及 Levin 和 Wen 的弦网模型。 每个任意子都与可观测量代数的超选择扇区相关。 对超选择扇区的分析允许人们恢复完整的任意子结构，包括粒子融合和编织。 在物理允许的扰动下，我们将研究超选择扇区以及粒子融合和编织的稳定性。 任意子的稳定性是容错量子计算中一个重大方案——拓扑量子计算的前提。 该项目的结果构成了通过拓扑有序态继续寻找通用量子计算机的基础。 该 NSF EAPSI 奖项是与日本科学振兴会合作资助的。