Physical Properties of Strongly Correlated Quantum Liquids

这笔拨款支持基本凝聚态物理的理论研究。凝聚态物理一直由两个主要主题主导。第一种是朗道的费米液体理论，第二种是朗道的对称性破缺理论和重整化群理论。最近的研究表明，凝聚态物理学正在出现新的主题。这项拨款支持的研究将探索这些新主题。其中一个新的发展是首席研究员(PI)引入的量子/拓扑序。拓扑序描述了分数量子霍尔态中的一种新的序。量子序描述了一百多种不同量子自旋液体的内部结构。量子/拓扑有序代表了朗道对称破缺理论所不能描述的新型有序。最近的研究表明，量子/拓扑有序与弦凝聚现象密切相关。量子/拓扑有序和弦凝聚理论仍处于初级阶段。本研究将试图发展出一套更完整的理论。特别是，将研究以下项目：弦凝聚理论有可能成为像朗道对称破缺理论那样发展成熟的理论。对称破缺状态背后的数学框架是群论。这个项目将试图揭示弦凝聚背后的数学框架。这一新知识将使我们对不同弦凝聚态之间的相变以及弦凝聚态上方的集体激发有一个系统的了解。这一新知识还将导致对不同弦凝聚态的分类。在先前的支持下，PI表明，只要FQH态包含非玻色中性准粒子，干净的FQH态之间就可以发生连续的跃迁。利用拓扑有序和弦凝聚之间的关系，我们将研究更一般的FQH态之间的连续跃迁，以及它们的实验结果。这些理论研究将对清洁FQH态之间的连续跃迁进行系统的实验研究。由于FQH态可以看作弦凝聚态，这些实验还可以揭示不同弦凝聚态之间的跃迁性质。它们的正常态包含类电子的准粒子。然而，准粒子的费米面是违反Luttinger定理的小片段。该项目将为这种奇怪的欠掺杂正常态发展一种理论。量子有序和相关的自旋液体将在研究中发挥关键作用。欠掺杂正常态的新理论将使人们更好地理解超导相变的机制和本质，这项研究将对物理学的许多领域产生广泛而深刻的影响。弦凝聚态具有健壮的量子纠缠，可用于执行容错量子计算。由于弦凝聚态的集体激发是规范玻色子和费米子，这加深了我们对基本粒子起源的理解。凝聚态物理一直由两个主要主题主导。第一种是朗道的费米液体理论，第二种是朗道的对称性破缺理论和重整化群理论。最近的研究表明，凝聚态物理学正在出现新的主题。这笔赠款支持的研究将探索这些新主题。*

This grant supports theoretical research on fundamental condensed matter physics. Condensed matter physics has been dominated by two primary themes. The first is Landau's Fermi liquid theory and the second is Landau's symmetry breaking theory along with renormalization group theory. Recent studies suggest that new themes are emerging in condensed matter physics. The research supported by this grant will explore these new themes.One of the new developments is the quantum/topological order introduced by the principal investigator (PI). Topological order describes a new kind of order in fractional quantum Hall (FQH) states. Quantum order describes the internal structure of over one hundred different quantum spin liquids. Quantum/topological order represents new types of order that cannot be described by Landau's symmetry breaking theory. More recent research indicates that quantum/topological order is closely related to the phenomenon of string condensation. The theory of quantum/topological order and string condensation is still in its infancy. This research will attempt to develop a more complete theory. In particular, the following projects will be studied:The theory of string condensation has a potential to become a well-developed theory like Landau's theory of symmetry breaking. The mathematical framework behind symmetry breaking states is group theory. This project will try to reveal the mathematical framework behind string condensation. The new knowledge will lead to a systematic understanding of phase transitions between different string condensed states as well as the collective excitations above string condensed states. The new knowledge will also lead to a classification of different string condensed states.Under prior support, the PI showed that a continuous transition between clean FQH states can occur as long as the FQH states contain non-bosonic neutral quasiparticles. Using the relationship between topological order and string condensation, continuous transitions between more general FQH states will be studied, as well as their experimental consequences. These theoretical studies will lead to systematic experimental studies of continuous transitions between clean FQH states. Since FQH states can be viewed as string condensed states, these experiments can also reveal the properties of transitions between different string condensations.The underdoped high Tc superconductors have some very unusual properties. Their normal state contains electron-like quasiparticles. However, the Fermi surfaces of the quasiparticles are small segments that violate the Luttinger theorem. This project will develop a theory for this strange underdoped normal state. The quantum order and the associated spin liquids will play a key role in the research. The new theory of the underdoped normal state will lead to better understanding of the mechanism and nature of the superconducting transition.The research accomplished under this grant will have a broad and deep impact on many areas of physics. The string condensed states have robust quantum entanglements that can be used to perform fault tolerant quantum computing. Since the collective excitations in a string condensed state are gauge bosons and fermions, it deepens our understanding of the origin of elementary particles.%%% This grant supports theoretical research on fundamental condensed matter physics. Condensed matter physics has been dominated by two primary themes. The first is Landau's Fermi liquid theory and the second is Landau's symmetry breaking theory along with renormalization group theory. Recent studies suggest that new themes are emerging in condensed matter physics. The research supported by this grant will explore these new themes.***