Emergent gauge structures in interacting condensed matter systems

微观物体的性质，如原子和分子，是由量子物理的特殊定律所控制的。在量子世界中，粒子通常表现为波，而波现象，如光，具有粒子般的属性。在某些情况下，这种量子行为在宏观物体中表现出来，影响（并改善！）我们的日常生活；激光器和固态电子设备就是典型的例子。这个提议是关于探索系统中的量子现象，包括固体、液体和气体，当大量的量子粒子非常强烈地相互作用时，就会出现这种现象。不寻常的事情发生了：在某些情况下，相互作用的系统可以表现得好像它们的基本成分（例如电子）分裂成新的粒子。这种现象被称为“分馏化”。电子的部分具有迷人的性质，对基础科学具有极大的兴趣。例如，当电子分裂成称为非阿贝尔任意子的粒子时，这些粒子有一个显著的特性，当一个粒子沿着一个环绕着另一个粒子时，它会转变成另一种类型的粒子。有趣的是，非阿贝尔任意子的这种奇异性质在分数化在量子计算中的实际应用中起着关键作用。本提案中概述的研究涉及这些迷人现象被认为发生的系统的理论描述。这些包括高温铜超导体、超冷原子气体和人工工程半导体结构。除了有助于解决潜在的智力挑战外，拟议研究的目的是帮助开发这些显著现象在量子计算和信息领域的实际应用。

Properties of microscopic objects, such as atoms and molecules, are governed by the peculiar laws of quantum physics. In the quantum world particles often behave as waves, and wave phenomena, such as light, acquire particle-like attributes. In some cases, this quantum behavior manifests itself in macroscopic objects and affects (and improves!) our everyday lives; lasers and solid-state electronic devices stand as standard examples. This proposal is concerned with exploring quantum phenomena in systems that include solids, liquids, and gases, which arise when very large numbers of quantum particles interact very strongly. Unusual things then happen: in some situations interacting systems can behave as if their elementary constituents (electrons, for example) splinter into new particles. This phenomenon is called ''fractionalization''. Fractions of the electron have fascinating properties and are of great interest to fundamental science. For example, in a scenario when the electron splinters into particles called non-abelian anyons, these particles have a remarkable property that when one particle is taken along a loop around another, it transforms into a particle of another type. Interestingly, this bizarre property of non-abelian anyons plays a key role in a proposed practical application of fractionalization to quantum computation. Research outlined in this proposal deals with theoretical descriptions of systems where these fascinating phenomena are thought to occur. These include high-temperature cuprate superconductors, ultra-cold atom gases and artificially engineered semiconductor structures. Besides contributing to resolving the underlying intellectual challenges the aim of the proposed research is to help develop practical applications of these remarkable phenomena in the area of quantum computation and information.