Exotic physics in quantum Hall and spin liquid systems

物质可能有哪些相？这是凝聚态物理的一个核心问题。历史上曾使用过两种组织原理：自由电子能带理论和自发对称性破缺理论。量子凝聚态物理学的一个现代主题是寻求理解这两种范式之外的相互作用的多体系统。两个突出的例子是分数量子霍尔效应和量子自旋液体。这些系统最显着的共同特征是电子分裂：在低温下，电子的行为就好像它们被“分裂”成更小的部分（例如具有分数电荷或统计数据的粒子）。这证明了涌现原理的力量：多体系统的集体行为可能与其微观成分截然不同。从现代的角度来看，电子分裂最终来自于长程量子纠缠。我的研究计划将侧重于更好地理解由于远程纠缠（例如碎片化）而产生的各种新兴现象。 在接下来的五年中，我想更好地理解（1）给定系统中允许的碎片化模式是什么？ （2）无序对分数化物理有何影响？最近的实验和理论发展很好地激发了这些问题。例如，问题 (1) 的自然背景是理解一个特别有趣的系统（称为 5/2 量子霍尔态）中不同可能的分数化模式。这个问题的答案将有助于明确地将 5/2 态建立为非阿贝尔拓扑序，这对于未来的量子信息处理可能有用。问题（2）是由量子自旋液体的研究引发的：在过去的十年中，已经发现了许多“候选”自旋液体材料，但其中大多数往往相当脏。因此，了解量子自旋液体中的无序效应对于连接理论与实验至关重要。 对多体系统中的长程量子纠缠的研究不仅本身具有深刻的概念价值，而且还可以为未来的技术发展铺平道路，从量子信息处理到具有以前未曾想象过的电特性的材料——就像自由电子和对称性破缺理论为半导体、磁体和超导体的物理学奠定了基础一样，所有这些都在上世纪的技术革命中发挥了重要作用。 该研究计划将培养大约四名博士。学生。他们将获得现代物理学的各种分析和数值技能（例如量子场论、统计力学和固态物理学）。更重要的是，他们将学会像物理学家一样思考和交流。所有这些都将有利于他们未来在学术界或技术相关行业的职业生涯。

What are the possible phases of matter? This is a central question of condensed matter physics. Historically two organizing principles have been used: the free electron band theory and the theory of spontaneous symmetry breaking. A modern theme of quantum condensed matter physics is the quest to understand interacting many-body systems beyond these two paradigms. Two prominent examples are the fractional quantum Hall effect and quantum spin liquids. The most striking common feature of these systems is electron fractionalization: at low temperature the electrons behave as if they are “split” into smaller fractions (such as particles with fractional electric charge or statistics). This demonstrates the power of the principle of emergence: the collective behavior of a many-body system can be drastically different from its microscopic constituents. From a modern point of view electron fractionalization ultimately come from long-range quantum entanglement. My research program will be focused on better understanding various emergent phenomena due to long-range entanglement such as fractionalization. In the next five years I would like to better understand (1) what are the allowed patterns of fractionalization in a given system? and (2) what are the effects of disorder on the physics of fractionalization? These questions are well motivated by recent experimental and theoretical developments. For example, a natural context for question (1) is to understand different possible patterns of fractionalization in a particularly interesting system known as the 5/2 quantum Hall state. An answer to this question would help establishing the 5/2 state unambiguously as a non-abelian topological order, potentially useful for future quantum information processing. Question (2) is motivated by the study of quantum spin liquids: during the past decade many "candidate" spin liquid materials have been discovered, but most of them tend to be rather dirty. An understanding of disorder effects in quantum spin liquids will therefore be crucial for bridging theories with experiments. The study of long-range quantum entanglement in many-body systems not only bears deep conceptual value on its own, but could also pave the way for future technological developments, ranging from quantum information processing to materials with previously unconceived electric properties - just like how the theories of free electrons and symmetry breaking laid the foundations for physics of semiconductors, magnets and superconductors, all of which played major roles in the technological revolution last century. This research program will train around four Ph.D. students. They will acquire various analytic and numerical skills in modern physics (such as those in quantum field theory, statistical mechanics and solid state physics). More importantly they will learn to think and communicate like physicists. All these will benefit their future career, in academia or in technology-related industry.