Theories for Novel States of Matter Observed and Constructed in Condensed Matter and Cold Atom Systems

该奖项支持在材料和在超低温下由单个原子排列组成的系统中出现的新物质状态的理论发展方面的研究和教育。这些系统中相互作用的粒子的量子力学行为产生了极其丰富的物理和概念奥秘，继续要求科学家更好甚至是革命性的理解。最近，在各种凝聚态物质系统中取得了意想不到的和令人兴奋的发现，例如由两片石墨烯片制成的器件，当两片石墨烯片以相对于彼此的特定方向精确堆叠时，可以表现出超导性。这些系统提供了前所未有的可调性，可能代表了量子多体物理研究新时代的开始。最近在冷原子实验技术方面的相关进展允许探索新的物理学：在某些条件下，例如在特定特征的激光照射下，这些系统的行为就好像它们存在于比我们通常的三维空间更高的维度空间中。本项目旨在发展和应用新的理论概念和方法来研究量子力学和多体物理在这些平台中的相互作用，并为它们在各种现象中的表现发展理论。这项研究可能会带来对自然的新的基本理解，也可能会带来利用这些严格的量子现象的技术创新。该项目具有超越凝聚态物理的潜在科学影响，因为该研究与高能物理相关。PI希望与相关领域的科学家进行广泛的互动和合作。该项目将提供培训和指导研究生和博士后研究人员的机会，为他们提供基本的理论工具，不仅可以应用于学术界的物理研究，而且可以在广泛的工业环境中找到用途。该奖项支持凝聚态和冷原子系统中非常规物质状态的研究和教育。该项目的目标有三个方面：i)通过PI小组最近开发的一种形式描述和理解最近发现的云纹超晶格中的超导性和弱相关绝缘体相，并在相关系统中设计更多奇特的物质状态；Ii)构建和理解物质的非常规状态，如强相互作用拓扑态和高维对称保护拓扑态，这些可以在具有合成维度的冷原子系统中实现；iii)使用完全可溶的Sachdev-Ye-Kitaev物理作为起点来描述和理解在高温超导体中实验观察到的非费米液体状态和相关现象。该项目具有超越凝聚态物理的潜在科学影响，因为该研究与高能物理相关。PI希望与相关领域的科学家进行广泛的互动和合作。该项目将提供培训和指导研究生和博士后研究人员的机会，为他们提供基本的理论工具，不仅可以应用于学术界的物理研究，而且可以在广泛的工业环境中找到用途。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

NONTECHNICAL SUMMARYThis award supports research and education on developing theories for new states of matter that appear in materials and in systems comprised of arrangements of individual atoms at ultralow temperatures. The quantum mechanical behavior of interacting particles in these systems generates extremely rich physics and conceptual mysteries that continue to demand better and even revolutionary understanding from scientists. Recently, unexpected and exciting discoveries have been made in various condensed matter systems, such as devices made from two graphene sheets that can exhibit superconductivity when the two sheets are precisely stacked at a specific orientation with respect to one another. These systems offer unprecedented tunability and may represent the beginning of a new era of study in quantum many-body physics. Related recent progress in cold-atom experimental techniques allows the exploration of novel physics: under certain conditions, e.g. illumination by laser light of specific characteristics, these systems behave as if they exist in a higher-dimensional space than our usual three dimensions. This PI aims to develop and apply new theoretical concepts and methodologies to study the interplay of quantum mechanics and many-body physics in these platforms, and to develop theories for their manifestations in a variety of phenomena. The research could potentially lead to both new fundamental understanding of nature, and also to technological innovation from harnessing these strictly quantum phenomena. The project has potential scientific impact beyond condensed matter physics, as the research is relevant for high-energy physics. The PI expects to interact and collaborate broadly with scientists from related fields. The project will offer opportunities for training and mentoring graduate students and of postdoc researchers, providing them with essential theoretical tools that not only can be applied in physics research within academia but can also find uses in a wide range of industrial settings.TECHNICAL SUMMARYThis award supports research and education on unconventional states of matter in condensed-matter and cold-atom systems. The goal of this project is three-fold: i) to describe and understand the recently discovered superconductivity and the weakly correlated insulator phase in moire superlattices via a formalism developed by the PI's group recently, and to also engineer more exotic states of matter in related systems; ii) to construct and understand unconventional states of matter such as strongly interacting topological states and symmetry-protected topological states in high dimensions that can be realized in cold atom systems with synthetic dimensions; iii) to use the exactly soluble Sachdev-Ye-Kitaev physics as the starting point to describe and understand non-Fermi-liquid states and related phenomena that are experimentally observed in high-temperature superconductors.The project has potential scientific impact beyond condensed matter physics, as the research is relevant for high-energy physics. The PI expects to interact and collaborate broadly with scientists from related fields. The project will offer opportunities for training and mentoring graduate students and of postdoc researchers, providing them with essential theoretical tools that not only can be applied in physics research within academia but can also find uses in a wide range of industrial settings.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.