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Exotic Phases and Loop Models in Condensed Matter

凝聚态物质中的奇异相和环模型

基本信息

批准号：
EP/F008880/1
负责人：
John Cardy
金额：
$ 8.39万
依托单位：
University of Oxford
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2007
资助国家：
英国
起止时间：
2007 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FF008880%2F1
关键词：
Exotic Phases Loop Models Condensed

项目摘要

A topic of great current interest in both theoretical and experimental condensed matter physics is the search for 'exotic' phases. Such phases exist in two-dimensional electron gases, and there is substantial evidence that they also occur in certain kinds of magnets. Many efforts are focused on systems in two spatial dimensions. Much is understood theoretically about one-dimensional systems, but seeing their behaviour in the lab is very difficult. Systems effectively in two dimensions have even more rich theoretical possibilities than in one, and are also easier to realise. A famous example is the quantum Hall effect, which arises when a two-dimensional electron gas is placed in a strong magnetic field. One spectacular experimentally verified prediction was the appearance of fractional charge. This means that even though the system is made up entirely of electrons, there are quasiparticles whose charge is a fraction of an electron. For example, in the simplest case, removing one electron from the system creates three identical localized 'quasiparticles', which necessarily have charge one third of the electron's.One motivation for studying exotic phases is to find a system capable of acting as a topological quantum computer. The general idea of quantum computation is to exploit peculiar properties of quantum mechanics to build a new sort of computer, able to solveproblems too large for a conventional computer. A quantum computer, for example, could factor much larger numbers than conventional ones, enabling commonly used encryption schemes to be cracked. Many obstacles stand in the way of actually building a quantum computer, the most substantial being that most approacheswould require devising a system capable of repeatedly producing results accurate on the order of one part in 100,000. While such precision is not inconceivable, the difficulty in doing so has resulted in a great deal of interest in topological quantum computation, which avoids this difficulty. The 'qubits' (or quantum bits, which are processed in the elementary steps of a computation) of a topological quantum computer are formed from particles with fractional charge.Of course, studying new problems often involves developing new theoretical tools. Fortunately some of these are at hand, using mathematics developed only in the last few years. This gives us new ways of describing the microscopic behaviour of many of these systems in term of their geometrical properties - from certain points of view they look like a tangled mass of spaghetti, or random curves. The precise characterisation of these random curves will give us access to the large scale properties of the exotic phases we wish to understand. There are several other powerful theoretical methods which can by brought to bear, in which the investigators and the visiting researcher, between them, have a great deal of experience.

在凝聚态物理学的理论和实验中，一个非常有趣的话题是寻找“奇异”相。这种相存在于二维电子气体中，并且有大量证据表明它们也存在于某些类型的磁体中。许多努力都集中在两个空间维度的系统。理论上对一维系统有很多了解，但在实验室中观察它们的行为是非常困难的。在二维中有效的系统比在一维中更有丰富的理论可能性，也更容易实现。一个著名的例子是量子霍尔效应，当二维电子气被置于强磁场中时就会产生这种效应。一个壮观的实验验证的预测是分数电荷的出现。这意味着即使系统完全由电子组成，也有准粒子的电荷是电子的一小部分。例如，在最简单的情况下，从系统中移除一个电子会产生三个相同的局域化“准粒子”，它们的电荷必然是电子的三分之一。研究奇异相的一个动机是找到一个能够充当拓扑量子计算机的系统。量子计算的基本思想是利用量子力学的特殊性质来建造一种新型计算机，能够解决传统计算机无法解决的问题。例如，量子计算机可以分解比传统计算机大得多的数字，从而使常用的加密方案能够被破解。许多障碍阻碍了实际建造量子计算机的道路，最重要的是，大多数方法都需要设计一个能够重复产生精确到十万分之一的结果的系统。虽然这样的精确度并不是不可想象的，但这样做的困难导致了对拓扑量子计算的极大兴趣，这避免了这种困难。拓扑量子计算机的“量子比特”（或量子比特，在计算的基本步骤中处理）是由具有分数电荷的粒子形成的。当然，研究新问题通常涉及开发新的理论工具。幸运的是，其中一些是手头上，使用数学发展只是在过去几年。这给了我们新的方法来描述这些系统的微观行为，从它们的几何性质来看，它们看起来像一团纠结的意大利面条，或者随机曲线。这些随机曲线的精确表征将使我们能够获得我们希望了解的奇异相位的大尺度特性。还有其他几种强有力的理论方法可以使用，调查人员和访问研究人员在这方面都有丰富的经验。