Exotic Quantum Criticalities in Low Dimensions and Systems with Unusual Quantum Many-Body Thermalization

非技术总结该奖项支持研究涉及许多量子粒子的奇异集体行为的理论研究。 在绝对零度下，这样的系统可以组织成无数的物质量子态--量子相--这取决于粒子之间相互作用的细节。 虽然最常见的相和它们的转换是很好理解的，但一些量子相变不适合传统的范式，最值得注意的是在量子磁体中可能发生的具有不匹配顺序的相之间的连续转变。 然而，另一类相-所谓的无隙自旋液体与紧急巡回准粒子-提出发生在几个反铁磁固体，无视秩序，即使在零温度。 (Here，“液体”指的是固体内部电子磁性方向的随机性。 PI的小组将在一维和二维中追踪这种不寻常的量子相变的易处理的例子，以及最近在候选自旋液体材料中的实验所激发的问题。集体量子行为的另一个方面是当许多粒子的系统在零温度以上的非平衡态中开始时的演化。 这一点已经引起了人们的注意，因为实验主义者是具有许多自由度的工程系统，这些自由度表现为量子力学，部分原因是为了开发量子技术。 描述这种演化的一个基本思想是动力学热化和密切相关的本征态热化假设，它提供了一种理解为什么时间只在一个方向上流动的方法。 热化的一个显著例外-所谓的多体定域化-发生在存在大量杂质的情况下。 一个具有挑战性的问题，也是技术上的兴趣，是热化是否可以完全或至少非常强烈地抑制在没有杂质的情况下。 PI的团队将继续致力于理解前热化现象，以及违反本征态热化假设的所谓量子多体疤痕态。该奖项下的项目将引导研究生在量子多体疤痕态的前沿进行研究。粒子物理学，并将教他们各种分析和数值方法，这将为他们在量子物理学和量子工程未来的职业生涯做好准备该奖项支持研究量子多体物理学不同方面的理论研究：1）非常规的量子相变和零温度下的临界相，2）在零温度以上非零能量密度下的不寻常的热化动力学。1）虽然到目前为止，我们已经有了无数间隙相的良好的“定点”图像，包括常规的和奇异的，在很多情况下，我们对量子相变的理解并不是很好。 其中，超越朗道范式的所谓“去限制量子临界点”已经吸引了研究人员超过15年;然而，找到真正受控的这种临界点的实例一直存在争议。 另一个具有挑战性的开放问题是描述无间隙的细分阶段，这被认为是不需要微调的关键阶段。 PI的团队将在低维中寻找非常规量子临界点的易处理的例子，并将追求最近在候选无间隙自旋液体材料中的实验所激发的项目。 多年来，对这些问题的兴趣主要是理论上的，因为它们涉及统计力学的基础和量子混沌的概念。 然而，工程量子系统的现代实验，如冷原子阵列、囚禁离子、偶极自旋杂质等，已经实现了具有许多量子自由度的良好隔离系统，并且已经发现了意想不到的现象，在该领域开辟了新的令人兴奋的方向。 在这种情况下，PI的小组将特别追求在没有无序的系统中不寻常的热化的例子，并将探索预热化和量子多体疤痕状态的问题。 PI的团队研究具体的系统来解决具有挑战性的开放性问题，并结合和开发分析和数值工具来实现这一目标。该奖项下的项目将引导研究生在凝聚态物理的前沿进行研究。 学生将学习量子多体系统的各种分析和数值方法，为他们未来在量子物理和量子工程领域的职业生涯做好准备。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

NON-TECHNICAL SUMMARYThis award supports theoretical research studying exotic collective behaviors involving many quantum particles. At absolute zero temperature, such systems can organize into myriad quantum states of matter---quantum phases---depending on details of interactions between particles. While the most common of such phases and their transformations are well understood, some quantum phase transitions do not fit into conventional paradigms, most notably continuous transitions between phases with mismatched orders as can occur in quantum magnets. Yet another class of phases---so-called gapless spin liquids with emergent itinerant quasiparticles---are proposed to occur in several antiferromagnetic solids that defy ordering even at zero temperature. (Here, "liquid" refers to randomness in the directions of the electrons' magnetism inside a solid.) The PI's group will pursue tractable examples of such unusual quantum phase transitions in one and two dimensions and also questions motivated by recent experiments in candidate spin-liquid materials.A different aspect of collective quantum behavior is evolution in time when a system of many particles is started in a non-equilibrium state with finite energy density above zero temperature. This has come to the fore as experimentalists are engineering systems with many degrees of freedom that behave quantum-mechanically, in part in an effort to develop quantum technologies. A fundamental idea to describe such an evolution is that of dynamical thermalization and the closely related eigenstate thermalization hypothesis, which offers a way of understanding why time flows only in one direction. A notable exception to thermalization---so-called many-body localization---occurs in the presence of a large number of impurities. A challenging question, also of technological interest, is whether thermalization can be completely or at least very strongly suppressed in the absence of impurities. The PI's group will continue work on understanding pre-thermalization phenomena and also on so-called quantum many-body scar states that violate the eigenstate thermalization hypothesis.Projects under this award will initiate graduate students to research at the frontier of quantum many-particle physics and will teach them a variety of analytical and numerical approaches that will prepare them for future careers in quantum physics and quantum engineering areas.TECHNICAL SUMMARYThis award supports theoretical research studying different facets of quantum many-body physics: 1) unconventional quantum phase transitions and critical phases at zero temperature, and 2) unusual thermalization dynamics at non-zero energy density above zero temperature.1) While by now we have good ``fixed-point'' pictures of myriad gapped phases, both conventional and exotic, we do not have as good an understanding of quantum phase transitions in many cases. Among these, so-called ``deconfined quantum critical points'' that lie beyond the Landau paradigm have fascinated researchers for more than fifteen years; however, finding truly controlled instances of such critical points has been controversial. Another challenging open problem is the description of gapless fractionalized phases, which are believed to be critical phases that do not require fine-tuning. The PI's group will search for tractable examples of unconventional quantum critical points in low dimensions and will also pursue projects motivated by recent experiments in candidate gapless spin-liquid materials.2) This award will also pursue research in quantum many-body dynamics and thermalization in closed quantum systems. For many years, the interest in such questions had been primarily theoretical, as they relate to foundations of statistical mechanics and notions of quantum chaos. However, modern experiments in engineered quantum systems such as cold atom arrays, trapped ions, dipolar spin impurities, etc., have already achieved well-isolated systems with many quantum degrees of freedom, and are already finding unexpected phenomena opening new exciting directions in the field. In this context, the PI's group will specifically pursue examples of unusual thermalization in systems without disorder and will explore questions of pre-thermalization and quantum many-body scar states. The PI's group studies concrete systems to address challenging open questions and combines and develops both analytical and numerical tools to achieve this.Projects under this award will initiate graduate students to research at the frontier of condensed-matter physics. The students will learn a variety of analytical and numerical approaches to quantum many-body systems that will prepare them for future careers in quantum physics and quantum engineering areas.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.