Are Itinerant-Electron Quantum Critical Points Intrinsically Multicritical?

表面上简单的固体的电子行为可以产生巨大的技术影响。举一个最近的例子，某些层状材料的巨磁电阻迅速从实验发现转移到理论理解，然后成为现代硬盘驱动器的科学基础。除了技术上的重要性外，这种在表面上简单的材料中发生的意料之外的行为为基础物理学提供了一个重要的实验窗口。理论物理学家面临的一个中心挑战是确定许多相互作用的电子的集体量子行为。在这一过程中取得了沿着显著的成功--朗道和费米的理论（称为朗道-费米液体理论）表明，在许多情况下，即使电子之间的相互作用很强，它们的行为几乎就像它们没有相互作用一样，但具有修改过的个体特性。然而，已经发现了大量（并且越来越多）的材料，它们的电子行为不能用朗道-费米液体理论描述。物理学家一直在努力制定一个统一的图片来解释这些非费米液体材料。量子临界性理论的提出是一个巨大的飞跃。该理论描述了在经典和量子行为之间精细平衡的系统的行为-通常是接近零温度磁相变的系统，即当某些参数（如压力）在接近绝对零度时，系统显示出从磁性到非磁性行为的变化。大量的材料都可以用量子临界理论来描述，但近年来，人们发现量子临界理论存在一些问题。每当人们试图在非常接近零温度点的地方进行实验时，磁行为的转变应该发生，人们发现一些非常不同的东西-通常电子以完全不同的方式组织。与此同时，理论物理学家已经意识到，被认为描述磁量子相变的数学并不是自洽的。这种不一致性并不小-它表明我们对强相关系统的理解出现了根本性的崩溃。物理学家们的希望是，在解决这些问题的过程中，将导致对集体量子行为本质的更广泛的新理解。这是一个特别富有成果的时期，因为许多理论和实验成分已经到位，并且已经成熟，可以结合起来形成新的理论。这些想法不仅适用于电子系统，而且适用于其他具有许多相互作用量子粒子的系统。对被激光和磁场限制的超冷原子的研究，也许为这些想法的实验研究提供了一个更清晰的论坛。如上所述，这项工作不仅对我们对世界的基本理解很重要，而且很可能直接用于技术。随着我们对纳米世界的操纵使我们越来越深入量子领域，我们必须了解它的本质。

The electronic behaviour of apparently simple solids can have enormous technological impact. To take a recent example, the giant magnetoresistance of certain layered materials rapidly moved from experimental discovery to theoretical understanding and then to the scientific underpinning of modern hard drives. As well as its technological importance, the occurrence of such unanticipated behaviour in apparently simple materials provides a vital experimental window upon fundamental physics.A central challenge facing theoretical physicists is to determine the collective quantum behaviour of many interacting electrons. There have been notable successes along the way- the theory of Landau and Fermi (known as Landau-Fermi-liquid theory) showed that in many situations, even if the electrons interact strongly, they behave almost as though they were not interacting, but with modified individual characteristics. However, a large (and increasing) number of materials have been discovered whose electronic behaviour cannot be described by the Landau-Fermi-liquid theory. Physicists have struggled to formulate a unified picture to explain these non-Fermi liquid materials. A great leap forwards was made with the formulation of the theory of quantum criticality. This theory describes the behaviour of systems that are finely balanced between classical and quantum behaviour- usually systems that are near to a zero-temperature magnetic phase transition i.e. systems that show a change from magnetic to non-magnetic behaviour as some parameter such as pressure is varied at close to absolute zero. A large number of materials appear to be described by the theory of quantum criticality.In recent years, problems have been found in this theory. Whenever one tries to perform experiments very close to the point at zero temperature where the transition in magnetic behaviour ought to occur, one finds something very different- often the electrons are organised in a completely different way. At the same time, theoretical physicists have realised that the mathematics which was thought to describe the magnetic quantum phase transition is not self-consistent. This inconsistency is not minor --- it suggests a fundamental breakdown in our understanding of strongly correlated systems. The hope amongst physicists is that in resolving these issues a new broader understanding of the nature of collective quantum behaviour will result. This is a particularly fruitful time for such investigations as a number of theoretical and experimental ingredients are in place and ripe for combining to form the new theory.These ideas apply not only to electron systems, but also to other systems with many interacting quantum particles. The investigation of ultra-cold atoms confined by a combination of lasers and magnetic fields presents perhaps a cleaner forum for the experimental investigation of these ideas. As indicated above, not only is this work important our fundamental understanding of the world, it is also likely to feed directly into technology. As our manipulation of the nano-world leads us further and further into the quantum realm, it is imperative that we understand its nature.