Physical Properties of Strongly Correlated Quantum Liquids

该补助金支持基础凝聚态物理学的理论研究。 凝聚态物理学一直被两个主要主题所主导。 第一个是朗道的费米液体理论，第二个是朗道的对称性破缺理论沿着重整化群理论。 最近的研究表明，凝聚态物理学正在出现新的主题。 这项资助所支持的研究将探索这些新的主题。其中一个新的发展是由首席研究员（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。 量子序描述了超过一百种不同的量子自旋液体的内部结构。 量子/拓扑序代表了朗道对称性破缺理论无法描述的新类型的序。 最近的研究表明，量子/拓扑秩序与弦凝聚现象密切相关。 量子/拓扑序和弦凝聚的理论仍处于起步阶段。 这项研究将试图发展一个更完整的理论。 特别是，以下项目将被研究：弦凝聚理论有潜力成为一个像朗道的对称性破缺理论发展良好的理论。 对称破缺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。 这些新的知识将导致对不同弦凝聚态之间的相变以及弦凝聚态以上的集体激发的系统理解。 新的知识也将导致不同的弦凝聚态的分类。在先前的支持下，PI表明，只要BHH态包含非玻色子中性准粒子，干净的BHH态之间就可以发生连续跃迁。 利用拓扑序与弦凝聚之间的关系，我们将研究更一般的C3 H态之间的连续跃迁，以及它们的实验结果。 这些理论研究将导致系统的实验研究之间的连续转换干净的CNOH状态。 由于超导体中的H2O H态可以看作是弦凝聚态，因此这些实验也可以揭示不同弦凝聚态之间的跃迁性质。 它们的正常状态包含类电子准粒子。 然而，准粒子的费米表面是违反卢廷格定理的小段。 这个项目将为这种奇怪的低掺杂正常状态发展一个理论。 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导致更好地理解超导转变的机制和性质。在此资助下完成的研究将对物理学的许多领域产生广泛而深刻的影响。 弦凝聚态具有鲁棒的量子纠缠，可以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，它加深了我们对基本粒子起源的理解。 该补助金支持基础凝聚态物理学的理论研究。 凝聚态物理学一直被两个主要主题所主导。 第一个是朗道的费米液体理论，第二个是朗道的对称性破缺理论沿着重整化群理论。 最近的研究表明，凝聚态物理学正在出现新的主题。 这项研究将探索这些新的主题。*

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.***