Quantum Phases and Transitions

该奖项支持量子相和相变的理论研究和教育，以及PI不断努力通过各种工具（如暑期学校课程、对话、公开讲座、书籍和评论文章）将该领域的发展传达给广泛的受众。当系统的基态随着哈密顿量参数的变化而发生相位变化时，比如从超导体到绝缘体，量子相变就发生了。与跃迁同样有趣的是相本身：它们支持的激发、它们的简并以及它们对外部探测的响应。PI为此开发了两种工具：(i)费米子的重整化群，其中费米表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最终特性（ii）和分数量子霍尔效应的哈密顿理论，这是对问题的算子处理，允许计算间隙，松弛率等。他计划在许多方面扩展和应用重整化群：描述奇异库仑相互作用，描述铁磁性，描述具有多个动量方向的费米子，描述如何同时为玻色子和费米子以及双层石墨烯制定重整化群这一恼人但重要的问题。他计划应用哈密顿理论来描述霍尔系统在半填充时对微波辐射的响应。最后，他建议在几个晶格上的李群和费米子运动之间寻找一个相当诱人的联系——在这些晶格上，李群产生了晶格并决定了它不寻常的光谱。PI计划通过评论文章、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的量子场论方法），继续向国内外广泛的受众传播思想，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。他将继续积极地将他关于重整化群的工作传播给姐妹学科，如核物理学和粒子物理学，这些学科已经将重整化群用于描述有限密度的物质。该奖项支持量子相变和物质量子态的理论研究和教育。不像我们更熟悉的相变，如水到蒸汽，量子相变发生在绝对零度的温度下，因为一个外部变量，如压力，在从一个相到另一个相的转变中被调整。人们认为，这些相变可以在很宽的温度范围内影响材料的电子特性，并有望解释某些类别材料的异常电子特性。PI将进一步发展和应用一项强大的技术，该技术最初是在粒子物理学中发展起来的，后来应用于相变理论。这种技术被称为重整化群，它使人们能够跨越扩展的长度尺度来检验理论中包含的物理。虽然这种方法对凝聚态物质和材料物理学的许多重要问题产生了深刻的见解，但它在其他方面的应用被证明更加困难。PI的目标是清除概念上的障碍，并收获它为量子相变和相互作用粒子的量子力学系统提供的有价值的见解。PI计划通过评论文章、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的量子场论方法），继续向国内外广泛的受众传播思想，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。他将继续积极地将他关于重整化群的工作传播给姐妹学科，如核物理学和粒子物理学，这些学科已经将重整化群用于描述有限密度的物质。

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.