Dynamics and entanglement near quantum phase transitions

物质通过相变来改变状态。在我们通常的经验中，这发生在温度超过阈值时，例如水在0°C变成冰。然而，更奇怪的转变可以通过首先将材料冷却到接近绝对零度的最低温度(−273°C)来实现。在那里，支配电子行为的量子力学定律占据主导地位，由量子效应而不是热效应驱动的跃迁发生。我的研究将针对这种量子相变，这可以通过向材料施加磁场、改变其化学成分或压缩来实现。例如，一些绝缘材料在很低的温度下具有磁性，但当通过改变化学成分添加足够多的移动载流子时，它们就变成了金属，失去了磁性。在绝缘体到金属的量子相变附近出现了一个不寻常的现象：系统变成了超导体，其中的电子形成对，在没有电阻的情况下传播。这种现象不能用超导的标准理论来解释，当材料被加热到绝对零度以上~100°C时，这种现象仍然很稳定。尽管潜在的机制仍不清楚，但有证据表明，它与系统在磁性绝缘体和金属之间处于“混淆”状态的量子涨落有关。 我的团队的理论研究将有助于揭示这种量子相变附近量子材料的物理性质，在这种相变中，会出现新的物质状态。这是一个具有挑战性的计划，因为这些转变附近相互竞争的阶段之间的强烈波动会导致长期激发的破坏。电子的“舞动”模式变得非常错综复杂，使遥远的伙伴纠缠在一起。我们将致力于回答相应的问题：一个没有长期激励的系统如何动态地对各种扰动做出反应？其多体“舞动模式”的本质特征是什么？我们如何利用它们来改进量子材料的数值模拟？我们的研究将利用量子多体理论中的尖端工具，包括数值模拟。我们将借鉴相关的见解，其他学科，如量子信息，甚至弦理论。 同样，关于冰川融化等普通相变的知识对社会也很重要，关于它们的量子相变的知识也变得至关重要。事实上，对量子相变的理解有望解释尖端材料中复杂而引人注目的现象，如高温导电性。这些材料的潜在应用范围从低成本的电力传输到坚固的量子计算机。

Matter changes states by undergoing phase transitions. In our common experience, this occurs as the temperature goes through a threshold, such as water turning into ice at 0 °C. However, more exotic transitions can be realized by first cooling a material down to the lowest accessible temperatures, near absolute zero (−273 °C). There the laws of quantum mechanics governing the behavior of the electrons become dominant, and transitions driven by quantum effects instead of thermal ones occur. My research will target such quantum phase transitions, which can be realized by applying a magnetic field to the material, changing its chemical composition, or by compressing it. For example, some insulating materials possess magnetic order at very low temperatures but when enough mobile charge carriers are added by varying the chemical composition, they become metallic and loose their magnetism. An extraordinary phenomenon occurs near this insulator-to-metal quantum phase transition: the system becomes a superconductor in which the electrons form pairs that travel without resistance. This phenomenon cannot be explained with the standard theory of superconductivity, and remains robust as the material is heated up to ~ 100 °C above absolute zero. Although the underlying mechanism is still not well-understood, evidence suggests that it is connected to the quantum fluctuations of the system in its “confused” state between a magnetic insulator and a metal. The theoretical research of my group will shed light on the physical properties of quantum materials in the vicinity of such quantum phase transitions, where novel states of matter emerge. This is a challenging program because the strong fluctuations between the competing phases near these transitions lead to the destruction of long-lived excitations. The “dancing” patterns of the electrons become highly intricate and entangle very distant partners. We will aim to answer the consequential questions: How does a system without long-lived excitations dynamically respond to various perturbations? What are the essential features of its many-body “dancing patterns”, and how can we exploit them to improve numerical modeling of quantum materials? Our research will make use of cutting edge tools in quantum many-body theory, including numerical simulations. We will borrow pertinent insights other disciplines such as quantum information and even string theory. In the same way that knowledge about ordinary phase transitions like the melting of ice is important to society, knowledge about their quantum counterparts is becoming crucial. Indeed, the understanding of quantum phase transitions holds the promise to explain complex and striking phenomena in cutting edge materials, such as high temperature conductivity. Potential applications of these materials range from the low cost transport of electricity, to robust quantum computers.