Dynamics and entanglement near quantum phase transitions

物质通过发生相变而改变状态。在我们的共同经验中，这种转变发生在温度超过一个阈值时，例如水在0摄氏度时变成冰。然而，更奇特的转变可以通过首先将材料冷却到接近绝对零度（273摄氏度）的最低温度来实现。在那里，控制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，它可以通过对材料施加磁场，改变其化学成分或压缩它来实现。例如，一些绝缘材料在非常低的温度下具有磁性，但当通过改变化学成分加入足够的移动电荷载流子时，它们就会变成金属并失去磁性。在这种绝缘体到金属的量子相变附近发生了一种非同寻常的现象：系统变成了超导体，其中电子形成对，没有阻力地移动。这种现象不能用超导的标准理论来解释，并且在材料被加热到绝对零度以上~ 100℃时仍然保持稳定。尽管潜在的机制还没有被很好地理解，但有证据表明，它与系统在磁性绝缘体和金属之间的“混乱”状态下的量子涨落有关。******我的小组的理论研究将阐明在这种量子相变附近的量子材料的物理性质，在那里物质的新状态出现。这是一个具有挑战性的程序，因为在这些转变附近的竞争相之间的强烈波动会导致长寿命激励的破坏。电子的“舞蹈”模式变得高度复杂，并纠缠在非常遥远的伙伴中。我们将致力于回答相应的问题：一个没有长寿命激励的系统如何动态响应各种扰动？它的多体“舞蹈模式”的基本特征是什么？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的尖端工具，包括数值模拟。我们将借鉴其他学科的相关见解，如量子信息甚至弦理论。******就像了解冰融化等普通相变对社会的重要性一样，了解量子相变也变得至关重要。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，如高温电导率。这些材料的潜在应用范围从低成本的电力传输到强大的量子计算机。

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.