Quantum Phases and Transitions

量子相和跃迁

• 批准号: 0901903
• 负责人: Ramamurti Shankar
• 金额: $ 37.5万
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-15 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0901903&HistoricalAwards=false
• 关键词: Quantum; Phases; Transitions

TECHNICAL SUMMARYThis award supports theoretical research and education on quantum phases and phase transitions as well as the PI's constant efforts to communicate developments in his field to a wide audience using a variety of vehicles like summer school courses, dialogs, public lectures, books, and review articles.Quantum phase transitions occur when the ground state of a system undergoes a change of phase, say from superconductor to insulator, in response to a changing parameter in the Hamiltonian. Equally interesting as the transitions, are the phases themselves: the excitations they support, their degeneracies and their responses to external probes. The PI has developed two tools to this end: (i) the renormalization group for fermions in which low-energy states near the Fermi surface are systematically eliminated to display the ultimate properties of the ground state and its instabilities (ii) and the Hamiltonian Theory of the Fractional Quantum Hall Effect which is an operator treatment of the problem that allows the computation of gaps, relaxation rates etc. He plans to extend and apply the renormalization group in many ways: to describe the singular Coulomb interaction, to describe ferromagnetism, to describe Fermions with more than one momentum direction normal to the Fermi surface, to describe the vexing but important problem of how to formulate a renormalization group for bosons and fermions at the same time and bilayer graphene. He plans to apply the Hamiltonian theory to describe the response of the Hall system near half-filling to microwave radiation. Finally he proposes to pursue a rather tantalizing connection between Lie groups and fermion motion on several lattices- where Lie groups generate the very lattice and determine its unusual spectrum.The PI plans to continue disseminating ideas here and abroad, to a broad audience, ranging from school children to advanced graduate students in summer schools, from professionals to the lay public via review articles, public lectures, web-based lectures, and his third text book, this time on the methods of quantum field theory in condensed matter physics. He will continue to actively disseminate his work on renormalization group to sister disciplines like Nuclear Physics and Particle Physics which have adapted it to describe matter at finite density.NON-TECHNICAL SUMMARYThis award supports theoretical research and education on quantum phase transitions and quantum states of matter. Unlike the more familiar phase transformations, like water to steam, quantum phase transitions occur at the absolute zero of temperature as an external variable, like pressure, is tuned through the transformation from one phase to another. It is believed that these phase transitions can influence the electronic properties of materials for a wide range of temperatures and hold promise to explain anomalous electronic properties of some classes of materials. The PI will further develop and apply a powerful technique first developed in particle physics but later applied to theory of phase transitions. The technique, called the renormalization group, enables one to examine the physics contained in a theory across expanding length scales. While this approach has yielded great insights into a number of important problems to condensed matter and materials physics, its application to others has proven more difficult. The PI aims to clear conceptual roadblocks and harvest the valuable insights it offers into quantum phase transitions and quantum mechanical systems of interacting particles more generally.The PI plans to continue disseminating ideas here and abroad, to a broad audience, ranging from school children to advanced graduate students in summer schools, from professionals to the lay public via review articles, public lectures, web-based lectures, and his third text book, this time on the methods of quantum field theory in condensed matter physics. He will continue to actively disseminate his work on renormalization group to sister disciplines like Nuclear Physics and Particle Physics which have adapted it to describe matter at finite density.

技术总结该奖项支持有关量子相变和相变的理论研究和教育，以及PI利用暑期课程、对话、公开讲座、书籍和评论文章等各种工具向广大受众传播其领域的发展的持续努力。量子相变发生在系统的基态随着哈密顿参数的变化而发生相变时，例如从超导体到绝缘体。与转变同样有趣的是阶段本身：它们支持的激发、它们的简并以及它们对外部探测的反应。PI为此开发了两个工具：(I)费米子的重整化群，其中费米面附近的低能态被系统地消除，以显示基态及其不稳定性的终极性质(Ii)和分数量子霍尔效应的哈密顿理论，该理论是对问题的算符处理，允许计算能隙、驰豫率等。他计划以多种方式扩展和应用重整化群：描述奇异库仑相互作用，描述铁磁性，描述垂直于费米面的一个以上动量方向的费米子，描述如何同时形成玻色子和费米子以及双层石墨烯的重整化群这一令人烦恼但又重要的问题。他计划应用哈密顿理论来描述接近半满的霍尔系统对微波辐射的响应。最后，他提议在李群和几个格子上的费米子运动之间建立一个相当诱人的联系--在这些格子上，李群生成格子并确定其不同寻常的光谱。PI计划继续在国内外传播思想，受众范围从小学生到暑期学校的高级研究生，从专业人士到普通公众，通过评论文章、公开讲座、网络讲座和他的第三本课本，这一次是关于凝聚态物理中量子场论的方法。他将继续积极地将他在重整化群方面的工作传播给姊妹学科，如核物理和粒子物理，这些学科已经使其适用于描述有限密度的物质。非技术总结该奖项支持关于量子相变和物质的量子态的理论研究和教育。与更常见的相变，如水到水蒸气的相变不同，量子相变发生在绝对零度的温度，因为外部变量，如压力，是通过从一个相到另一个相的转换来调节的。人们认为，这些相变可以在很大的温度范围内影响材料的电子性质，并有望解释某些类型材料的反常电子性质。PI将进一步发展和应用一项强大的技术，最初是在粒子物理学中开发的，但后来应用于相变理论。这项技术被称为重整化群，使人们能够在扩展的长度尺度上检查理论中包含的物理。虽然这种方法对凝聚态物质和材料物理的一些重要问题有了很好的见解，但它在其他方面的应用被证明是更加困难的。PI的目标是清除概念障碍，并在量子相变和更广泛的相互作用粒子的量子力学系统方面提供有价值的见解。PI计划继续向国内外广泛的受众传播想法，从小学生到暑期学校的高级研究生，从专业人士到普通公众，通过评论文章、公开讲座、网络讲座和他的第三本教科书，这一次是关于凝聚态物理中量子场论的方法。他将继续积极地将他在重整化群方面的工作传播给姊妹学科，如核物理和粒子物理，这些学科已经使其适用于描述有限密度的物质。