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-然而它们一直在我们身边，决定着我们世界中每一个物质的性质。量子物理定律定义了物质的每一种属性，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征。我们对这一影响链的理解是现代科学最伟大的成就之一。只有通过这种理解，科学家才能设计出现代技术和设备，如计算机、移动电话和光纤通信。在量子凝聚物质领域，我们在非常微观的尺度上关注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，并使新的应用成为可能。我们关注的一个关键概念是物质中的量子力学相干性。“连贯性”一词在这里意味着许多微观物体协同行动。当这种行为发生时，量子物理的效果就会大大增强。相干行为的一个主要例子发生在超导体中，在超导体中，由于量子力学的影响，电子可以以零电阻和零能量损失永远流动。在过去的几十年里，我们的社区已经变得很清楚，材料中的量子力学相干比我们之前预期的要普遍得多，尽管它的影响通常是微妙的，很好地隐藏在我们的视野中。了解由许多粒子(即物质)组成的系统中的相干效应是这项赠款支持的研究的主要目的。我们使用现代数学和计算工具的组合来研究我们领域的谜题。我们研究的物理是高度复杂的，因为在这样的系统中，许多组成粒子相互作用很强。其结果是，出现了本质上不同的行为。由于这些效应的新颖性，这一研究领域既具有挑战性，又令人兴奋，吸引了一些最优秀和最聪明的年轻科学家。我们将我们的努力分为三个主要主题：理解量子多体动力学：研究量子力学如何在微观尺度上影响材料系统的时间演化。我们的目标是确定关于一致性是如何创建、传播和销毁的新原则，以及这如何影响物质的属性。探索远离基态的量子行为：一个多世纪以来，人们一直认为，如果热能被放入一个物理系统中，它将不可避免地扩散到其他地区。然而，在过去的几年里，由于相互作用无序系统中量子相干的影响，增加的能量可能会以稳定的方式保持在一个区域内，这一点变得很清楚。我们的目标是更好地理解呈现这种稳定和/或相干的高能态的系统的性质。为量子相干现象确定拓扑平台：拓扑物质表现出微妙的长期相干模式，这是局部描述无法理解的。由于这些全球效应，这种材料被认为特别适合用于强大的量子计算应用。因此，对这些物质的研究吸引了来自物理、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位置，它们可能是如何设计的，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，就像一个世纪前基础半导体物理学的发现一样，我们的发现可能会使未来的技术革命成为可能。

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.