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二维自旋，玻色子和电子系统中的分馏相。这项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，以及对强相关材料（如铜高温超导体中的奇怪金属和假间隙相）中非费米液体流动电子态的观察。在铜酸盐和具有竞争相互作用的磁绝缘体的许多研究的刺激下，量子磁学领域经历了一个新的时代。量子自旋系统是多体物理的典型例子；概念上的发展之一是自旋液相的可能性。最近的一个突破是几个候选实验实现的出现，这些实验实现似乎是理论较少建立的无间隙自旋液体。提出的两种三角形晶格自旋液体材料的状态具有自旋子的费米表面，这是一种？旋转的金属”。PI的目的是确定这些材料在现有的理论框架内可以理解到什么程度。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流动的非费米电子液体。在适当的情况下，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。关注流动电荷扇区和从自旋液体研究中借鉴的从粒子方法使非微扰电荷液体的构建成为可能。？玻色金属。?PI将继续进行下一步，一个类似的电子系统项目，将自旋和电荷部门结合在一起。这项研究的一个重要目标是寻找这样的？自旋金属？”玻色金属，”和电子非费米液体在模型系统和指导数值研究。一种有前途的方法是利用准一维阶梯上的候选模型的受控DMRG研究，结合试验波函数和规范理论/玻色化分析，建立二维模型。PI还将研究物质场与2+1D规范场耦合的统计力学模型中的相变。这些是最近提出的量子磁体中竞争相之间的非常规量子临界点的有效场论。在这种规范理论中确立过渡的性质将使进一步的理论发展有更坚实的基础。PI还将研究具有统计相互作用的模型中的相和相变。该奖项支持理论研究和教育，旨在发现新的物质磁性状态，了解它们对高温超导体中出现的不寻常金属状态的影响，以及了解在标准相变理论之外可能发生的奇特转变。这项研究的动机和刺激是由于发现了具有不同寻常性质的新材料，挑战了凝聚态物理的传统范式。本研究的重点将是在材料和模型的实验室和计算机实验的背景下发展理论概念。这是一项基础研究，它为我们理解材料和物质的新状态奠定了知识基础，这些物质表现出我们目前理解之外的特性和奇异现象。这本身就是一项智力追求，其吸引力不亚于对宇宙的研究，但它也可能导致新现象和新设备技术的发现。

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.