RUI: Physics of Interacting Quantum Systems with Phase Transitions

非技术性总结该奖项支持具有许多相互作用粒子的量子系统的理论研究和教育。主要目标是确定的条件之间的组织的组成粒子的不同状态的转变的开始，并提出了一套建议，以检测这种转变的实验。在经典物理学中，当材料的温度达到临界点并且材料经历状态变化时，发生热相变，例如从水到冰的转变。在非常低的温度下，经典定律被打破，量子物理学取而代之。在这个层次上，不同的量子相可以从系统中不同相互作用之间的竞争中出现。不同的相与可以通过实验检测到的不同宏观性质相关联，例如良好或不良的导电性。这一研究课题与新材料的开发密切相关。物质的新阶段是新兴技术的关键组成部分，这可能会彻底改变我们使用和生产能源的方式，可能会导致新型电子设备，并可能促进量子计算机的规模扩大。发现物质的新相的潜在经济和社会影响是巨大的。该项目还将通过提供新的研究机会和物理学核心领域和计算方法方面的培训，促进妇女参与物理学，并改善叶史瓦大学斯特恩女子学院的教育基础设施。女本科生将继续与PI共同撰写论文，并在会议上传播其成果。来自当地高中的学生也将有机会体验斯特恩女子学院的研究。PI与她以前的三名学生合作，促进了这一努力，这些学生现在是女子高中的物理教师。此外，还计划扩大用于发布课程和研究成果的计算机程序的网页，这将有助于其他本科院校的教学和研究的整合。技术概要该奖项支持计算和分析方法的理论研究和教育，以提高我们对具有短程和长程相互作用的低维量子系统的理解。重点将放在两个有潜力开辟新的研究途径的主要课题上。分别是：1.确定了激发态量子相变的起始条件，并提出了一系列实验检测这种相变的建议。基态量子相变的研究对核物理、凝聚态物理和宇宙学等领域都至关重要。这一领域的进展可能是凝聚态物理学中未解决问题的关键，并可能导致物质的新相。最近，一个新的元素被带到了画面中：激发态量子相变的存在。它们主要在量子光学、分子和核物理学的模型中进行了研究。该项目将扩大分析范围，将凝聚态模型也包括在内。这将为理解多体凝聚态系统以及现有的激发态量子相变研究带来新的视角、工具和方法。探索通过增加相互作用的范围而不是增加现场无序或相互作用的幅度来实现局部化的违反直觉的情况。尽管有无数关于金属-绝缘体转变的研究，但这个主题仍然是部分理解的。这些转变通常分为两类：无序驱动的安德森转变和相互作用驱动的莫特转变。然而，目前的主要兴趣是在更丰富和更复杂的情况下，同时考虑相互作用和无序。通常的预期是，在存在长程相互作用的情况下，定位应该变得更加困难。然而，长程相互作用也可以导致子空间，在子空间内，状态是高度局域化的。该项目将探索新的方案，如后者，这将为本地化问题带来新的观点，该项目还将促进妇女参与物理学，并通过提供新的研究机会和物理学核心领域和计算方法的培训，改善叶史瓦大学斯特恩女子学院的教育基础设施。女本科生将继续与PI共同撰写论文，并在会议上传播其成果。来自当地高中的学生也将有机会体验斯特恩女子学院的研究。PI与她以前的三名学生合作，促进了这一努力，这些学生现在是女子高中的物理教师。此外，计划扩大一个旨在发布课程和研究成果的计算机程序的网页，这将有助于其他本科院校的教学和研究一体化。

NONTECHNICAL SUMMARYThis award supports theoretical research and education on quantum systems that have many interacting particles. The main goal is to identify the conditions for the onset of transitions between different states of organization of the constituent particles, and to put forward a set of proposals to detect such transitions experimentally. In classical physics, a thermal phase transition occurs when the temperature of a material reaches a critical point and the material undergoes a change in state, such as the transition from water to ice. At very low temperatures, classical laws break down and quantum physics takes over. At that level, different quantum phases can emerge from the competition between different interactions in the system. Distinct phases are associated with different macroscopic properties that can be experimentally detected, such as good or bad conductivity. This topic of research is tightly connected with the development of new materials. New phases of matter are critical components of emerging technologies, which may revolutionize how we use and produce energy, may lead to new types of electronic devices, and may facilitate the scaling up of quantum computers. The potential economical and social impact of the discovery of novel phases of matter is immense. Yet, one needs to know where to look to have a higher chance to find them.The project will also foster the participation of women in physics and improve the educational infrastructure at the Stern College for Women of Yeshiva University by offering new research opportunities and training in core areas of physics and in computational methods. Female undergraduate students will continue to coauthor papers with the PI and disseminate their results at conferences. Students from local high schools will also have the opportunity to experience research at Stern College for Women. This effort is facilitated by the PI's collaboration with three of her former students, who are now physics teachers in high schools for girls. Furthermore, the plan to expand a webpage designed for posting computer programs from courses and research findings will contribute to the integration of teaching and research at other undergraduate institutions.TECHNICAL SUMMARYThis award supports theoretical research and education on computational and analytical methods to advance our understanding of low-dimensional quantum systems with short- and long-range interactions. The focus will be on two main topics that carry potential to open new research avenues. They are:1. Identifying the conditions for the onset of quantum phase transitions at excited states and putting forward a set of proposals to detect such transitions experimentally. Studies of ground state quantum phase transitions are of crucial importance to fields as diverse as nuclear physics, condensed matter physics, and cosmology. Progress in this field may carry the key to unsolved problems in condensed matter physics and may lead to novel phases of matter. Recently, a new element has been brought to the picture: the existence of excited-state quantum phase transitions. They have mainly been examined in models from quantum optics, molecular and nuclear physics. This project will expand the analysis to also include condensed matter models. This will bring new perspectives, tools, and approaches to the understanding of many-body condensed matter systems as well as to the existing studies of excited-state quantum phase transitions.2. Exploring the counterintuitive scenario of achieving localization by increasing the range of the interactions, instead of increasing on-site disorder or the amplitude of the interactions.Despite innumerable studies about the metal-insulator transition, the subject is still partially understood. These transitions are usually divided in two categories: disorder-driven Anderson transitions and interaction-driven Mott transitions. The main current interest, however, is on the richer and more complicated case where both interaction and disorder are taken into account simultaneously. The usual expectation is that in the presence of long-range interactions, localization should become more difficult. Yet, long-range interactions can also lead to subspaces inside of which the states are highly localized. This project will explore new scenarios, such as the latter, which will bring a new viewpoint to the subject of localization.The project will also foster the participation of women in physics and improve the educational infrastructure at the Stern College for Women of Yeshiva University by offering new research opportunities and training in core areas of physics and in computational methods. Female undergraduate students will continue to coauthor papers with the PI and disseminate their results at conferences. Students from local high schools will also have the opportunity to experience research at Stern College for Women. This effort is facilitated by the PI's collaboration with three of her former students, who are now physics teachers in high schools for girls. Furthermore, the plan to expand a webpage designed for posting computer programs from courses and research findings will contribute to the integration of teaching and research at other undergraduate institutions.