Coherent Many-Body Quantum States of Matter

在我们的日常生活中，我们很少考虑量子力学的影响-然而它们却一直在我们身边，决定着我们世界中每一个物质对象的性质。量子物理学定律定义了物质的每一种性质，从单个原子的行为，到原子如何结合在一起形成材料，再到这些合成材料的特性。我们对这种影响链的理解是现代科学最伟大的胜利之一。只有通过这种理解，科学家们才能设计出现代技术和设备，如计算机、移动的电话和光纤通信。在量子凝聚态领域，我们关注的是微观尺度上的材料和物质的量子力学。我们的目标是发现新的原理，预测新的行为，新的物质类型，并实现新的应用。我们关注的一个关键概念是物质的量子力学相干性。这里的“一致性”一词意味着许多微观物体在一致地共同作用。当这种行为发生时，量子物理学的效果将大大增强。相干行为的一个主要例子发生在超导体中，由于量子力学的影响，电子可以永远流动，零阻力和零能量损失。在过去的几十年里，在我们的社区中，量子力学的相干性比我们以前预期的要普遍得多，尽管它的影响往往是微妙的，并且从我们的观点中隐藏得很好。理解由许多粒子组成的系统中的相干效应（即，物质）是这项拨款资助研究的主要目的。我们使用现代数学和计算工具的组合来研究我们领域的难题。我们研究的物理学是非常复杂的，因为在这样的系统中，许多组成粒子相互作用很强。因此，出现了性质上不同的行为。由于这些效应的新奇，这个研究领域既具有挑战性又令人兴奋，吸引了一些最优秀、最聪明的年轻科学家。我们将我们的努力分为三个主题：理解量子多体动力学：研究量子力学如何影响微观尺度上物质系统的时间演化。我们的目标是确定如何创建，传播和破坏相干性的新原则，以及这如何影响物质的性质。探索远离基态的量子行为：世纪以来，人们相信，如果热能在一个点上被放入物理系统，它将不可避免地扩散到其他区域。然而，在过去的几年里，由于相互作用的无序系统中的量子相干效应，增加的能量可能以稳定的方式保持在一个区域中。我们的目标是更好地了解系统的性能，目前这种稳定和/或相干的高能量状态。确定量子相干现象的拓扑平台：拓扑物质表现出微妙的长程相干模式，无法通过局部描述来理解。由于这些全局效应，这些材料被认为特别适合于稳健的量子计算应用。因此，对这些物质的研究吸引了来自物理学、数学和计算机科学的研究人员。我们将探索这些材料，它们在自然界中存在的地方，它们如何被工程化，以及它们的应用是什么。虽然我们的研究主要是学术性质的，但我们希望，类似于世纪前基础半导体物理学的发现，我们的发现可能会推动未来的技术革命。

In our everyday life we rarely think about the effects of quantum mechanics --- and yet they are constantly around us, determining the properties of every material object in our world. The laws of quantum physics define every property of matter, from the behaviour of individual atoms, to how the atoms bind together to form materials, to the characteristics of these resultant materials. Our understanding of this chain of influence is one of the greatest triumphs of modern science. It is only through this understanding that scientists have engineered modern technologies and devices such as computers, mobile phones, and fibre-optic communications. In the field of quantum condensed matter, we are concerned with materials, and the quantum mechanics of matter, at a very microscopic scale. Our aim is to uncover new principles, predict new behaviours, new types of matter, and enable new applications. A key concept that we focus on is the idea of quantum mechanical coherence in matter. The word "coherence" here implies that many microscopic objects are acting together in concert. Such behaviour, when it occurs, allows for the effects of quantum physics to be greatly enhanced. A prime example of coherent behaviour occurs in a superconductor, where due to the effects of quantum mechanics, electrons can flow forever with zero resistance and zero energy loss. In the last decades it has become clear in our community that quantum-mechanical coherence in materials is much more common than we previously expected, although its effects are often subtle and well hidden from our view. Understanding coherent effects in systems made of many particles (i.e., in material substances) is the main aim of the research supported by this grant. We use a combination of modern mathematical and computational tools to investigate the puzzles of our field. The physics we study is highly complex because in such systems, the many constituent particles interact strongly with each other. As a consequence, qualitatively different behaviour emerges. Because of the novelty of these effects, this field of study is both challenging and exciting, attracting some of the best and the brightest young scientists. We have divided our effort into three main themes: Understanding Quantum Many-Body Dynamics: the investigation of how quantum mechanics effects the time evolution of material systems on a microscopic scale. We aim to determine new principles for how coherence is created, spreads, and is destroyed, and how this affects the properties of the substance. Exploring Quantum Behaviour Far From the Ground State: for over a century it was believed that if heat energy is put into a physical system at one point, it will inevitably spread out to other regions. In the last few years, however, it has become clear that due to the effects of quantum coherence in interacting disordered systems, added energy may remain localized in one region in a stable fashion. We aim to understand better the properties of systems that present such stable and/or coherent high energy states. Identifying Topological Platforms for Quantum Coherent Phenomena: topological matter exhibits subtle long-range patterns of coherence that cannot be understood by local descriptions. Because of these global effects, such materials are believed to be particularly well suited for robust quantum computing applications. The study of these substances therefore has attracted researchers from physics, mathematics, and computer science. We will explore these materials, where they exist in nature, how they might be engineered, and what their applications are. While our research is mainly academic in nature, we hope that, analogous to discoveries in basic semiconductor physics a century ago, our discoveries may enable technological revolutions of the future.