Gapless Spin Liquids and Itinerant Non-Fermi-Liquids in Experiments and Models. Phase Transitions in Gauge-Matter Systems

该奖项支持理论研究和教育，以研究具有许多低能巡回激发的2D自旋，玻色子和电子系统中的分数相。本研究的动机是对最近发现的几种候选自旋液体材料的实验研究，以及对强关联材料（如铜氧化物高温超导体中的奇异金属相和赝能隙相）中非费米液体巡游电子态的观测。铜氧化物和对具有竞争相互作用的磁性绝缘体的大量研究推动了量子磁学领域的发展。量子自旋系统是多体物理学的典型例子;概念上的发展之一是自旋液相的可能性。最近的一个突破是出现了几个候选的实验实现，似乎是无隙自旋液体的理论是不太建立。两个三角形晶格自旋液体材料的一个建议的状态有一个费米表面的自旋子，这是一种？旋转金属”。PI的目标是确定在现有的理论框架内如何更好地理解这些材料。在了解了磁性背景下的这种不寻常状态之后，PI将应用这些想法来理解电子的巡回非费米液体。在铜酸盐的背景下，人们可以问，电荷自由度是否可以重新发挥作用，并研究这种奇怪的金属。专注于巡回收费部门，从自旋液体的研究借用从粒子的方法，使非微扰电荷液体的建设。?玻色金属？PI将采取下一步行动，为电子系统提供类似的计划，将自旋和电荷部门结合在一起。这项研究的一个重要推动力是寻找这样的？旋转金属”玻色金属，”和电子非费米液体在模型系统和指导数值研究。一个很有前途的方法是使用准一维阶梯上候选模型的受控DMRG研究结合试验波函数和规范理论/玻色化分析来建立2D。PI还将研究2+1D中物质场与规范场耦合的统计力学模型中的相变。这些出现作为最近提出的非常规量子临界点之间的量子磁体竞争阶段的有效场理论。在这种规范理论中建立跃迁的性质将使进一步的理论发展有更坚实的基础。非技术性总结该奖项支持旨在发现物质的新磁态的理论研究和教育，了解它们对高温超导体中出现的不寻常金属态的影响，并了解它们之间可能发生的位于相变标准理论之外的奇异转变。这项研究的动机和刺激的新材料的发现与不寻常的性质，挑战凝聚态物理学的传统范式。本研究的重点将是在实验室和计算机实验的材料和模型的背景下发展理论概念。这是基础研究，有助于我们理解材料和物质的新状态，表现出我们目前理解之外的属性和奇异现象的知识基础。这本身就是一种智力追求，不亚于对宇宙的研究，但它也可能导致新现象的发现和新的设备技术。

TECHNICAL SUMMARYThis award supports theoretical research and education to study fractionalized phases in spin, boson, and electron systems in 2D that have many low-energy itinerant excitations. This research is motivated by experiments on several recently discovered candidate spin-liquid materials, and from observations of non-Fermi-liquid itinerant electron states in strongly correlated materials such as the strange metal and pseudogap phases in the cuprate high temperature superconductors.The field of quantum magnetism has experienced a new era stimulated by the cuprates and by many studies of magnetic insulators with competing interactions. Quantum spin systems are prototypical examples of many-body physics; one of the conceptual developments is the possibility of spin liquid phases. A recent breakthrough is the appearance of several candidate experimental realizations which appear to be gapless spin liquids where theory is less established. A proposed state for two triangular lattice spin liquid materials has a Fermi surface of spinons, which is a kind of ?spin metal". The PI aims to determine how well these materials can be understood within the available theoretical frameworks.Having learned about such unusual states in the magnetism context, the PI will apply these ideas to understand itinerant non-Fermi-liquids of electrons. In the cuprate context, one can ask whether charge degrees of freedom can be put back into play and study the strange metal. Focusing on the itinerant charge sector, and slave-particle approaches borrowed from spin-liquid studies enable the construction of non-perturbative charge liquids. ?Bose metals.? The PI will pursue the next step, a similar program for electronic systems bringing together spin and charge sectors. An important thrust of this research is to search for such ?spin metals," ?Bose metals," and electronic non-Fermi-liquids in model systems and guide numerical studies. A promising approach is to build up towards 2D using controlled DMRG studies of candidate models on quasi-1D ladders combined with trial wavefunctions and gauge theory/bosonization analysis.The PI will also study phase transitions in statistical mechanics models with matter fields coupled to gauge fields in 2+1D. These arise as effective field theories for recently proposed unconventional quantum critical points between competing phases in quantum magnets. Establishing the nature of the transitions in such gauge theories will put further theoretical developments on firmer ground. The PI will also study phases and phase transitions in models with statistical interactions.NON-TECHNICAL SUMMARYThis award supports theoretical research and education that aims to discover new magnetic states of matter, to understand their implications for unusual metallic states that appear in high temperature superconductors, and to understand exotic transformations that can occur among them that lie outside the standard theory of phase transitions. This research is motivated and stimulated by the discovery of new materials with unusual properties that challenge conventional paradigms of condensed matter physics. The emphasis of this research will be on developing theoretical concepts in the context of laboratory and computer experiments on materials and models.This is fundamental research that contributes to the intellectual foundations of our understanding of materials and new states of matter that exhibit properties and exotic phenomena that lie outside our current understanding. This is an intellectual pursuit in its own right no less fascinating than the study of the universe, but it may also lead to the discovery of new phenomena and to new device technologies.