Analytical and numerical studies of novel fractionalized phases and unusual phase transitions

技术总结该奖项支持关于受挫量子磁铁中分级自旋液体相的理论研究和教育。这项研究受到了最近几个候选自旋液体材料的发现的刺激，这些材料的自旋位于二维和三维晶格上。PI的目标是使用Parton方法扩展这种细分相的可用波函数工具箱。在这种方法中，微观自旋或玻色子算符被分成辅助的类夸克场，这些场在平均场中被解禁闭，然后通过恢复物理希尔伯特空间的投影粘合在一起。除了流行的Gutzveler投影的从属费米子态外，PI还将使用投影的Schwinger玻色子波函数，这些波函数是磁性有序相附近的强候选者，以及由Majorana从属费米子方法激发的新波函数，该方法可以进一步丰富状态池中的无间隙自旋。另一个有趣的方向是可能与新的基于纠缠的数值方法相结合。在另一个推力中，PI将致力于更好地理解无间隙细分相，其中出现的规范场也是无间隙的，这是分析方法无法完全控制的一些最具挑战性的情况。PI将建立在具有纯环交换的模型中的激子玻色液体相的例子上，其中部分子规范方法可以完成，也可以与非部分子方法进行比较。这项研究将解决激子玻色液体理论中的一些公开问题，并将利用这些问题来了解无隙部分子规范系统。PI还将探索带有拓扑项的统计力学问题中的不寻常相变，将解析对偶方法和数值蒙特卡罗技术以一种强大的方式相结合。重点将放在具有相互统计相互作用的粒子的模型上。这样的模型出现在拓扑相及其相变的研究中，也出现在受挫量子反铁磁体的有效场论中。这项研究将有助于理解最近感兴趣的非传统量子相变。非技术总结该奖项支持专注于显示一种分馏现象的物质的不寻常量子状态的理论研究和教育。在某种意义上，电子就像是用自旋这个词来量化的微小的旋转顶端。它们还携带一个单位的电荷。当电子看起来像是分裂成两个独立的粒子时，分馏就会产生，一个有电荷但没有自旋，另一个有自旋但没有电荷。在实验上发现，电子在半导体界面的平面内运动，并暴露在强磁场中时，会出现分馏现象。长期以来，人们一直猜测材料中自然会出现类似的现象。最近发现了几个候选人。该项目旨在开发理论和计算工具箱，以发现和表征模型和实验材料中的分馏量子相。它还将研究在相变标准理论之外的这些状态之间可能发生的转换。材料中电子物质的新量子态的发现可能会带来新的技术。操纵电子物质的某些量子态可能会带来一种新的计算方式--量子计算，这种方法可能会比现有的计算机更强大。

TECHNICAL SUMMARYThis award supports theoretical research and education on fractionalized spin liquid phases in frustrated quantum magnets. The research is stimulated by recent discoveries of several candidate spin liquid materials with spins residing on two-dimensional and three-dimensional lattices. The PI aims to expand the available toolbox of wave functions for such fractionalized phases using a parton approach. In this approach, the microscopic spin or boson operator is split into auxiliary quark-like fields, which are taken to be deconfined in mean field and are then glued together by a projection recovering the physical Hilbert space. Besides popular Gutzwiller-projected slave fermion states, the PI will also use projected Schwinger boson wave functions that are strong candidates near magnetically ordered phases, as well as novel wave functions motivated from Majorana slave fermion approaches that can further enrich the pool of states with gapless spinons. Another interesting direction is possible combination with novel entanglement-based numerical approaches.In a separate thrust, the PI will work to develop a better understanding of gapless fractionalized phases where the emergent gauge fields are also gapless, which are some of the most challenging cases where analytical approaches are not under full control. The PI will build upon an example of an Exciton Bose Liquid phase in models with pure ring exchanges, where the parton-gauge approach can be brought to completion and also compared with non-parton approaches. The study will address a number of open questions in the Exciton Bose Liquid theory and will use these to learn about gapless parton-gauge systems.The PI will also explore unusual phase transitions in statistical mechanics problems with topological terms, combining analytical duality approaches and numerical Monte Carlo techniques in a powerful way. The focus will be on models with particles that have mutual statistical interactions. Such models arise in studies of topological phases and their phase transformations and also in effective field theories of frustrated quantum antiferromagnets. The research will help to understand unconventional quantum phase transitions of much recent interest.NON-TECHNICAL SUMMARYThis award supports theoretical research and education focusing on unusual quantum states of matter that show a kind of fractionalization phenomenon. In a sense, electrons are like tiny spinning tops quantified in the term spin. They also carry a unit of electric charge. Fractionalization results when electrons appear to behave as though they were split into two independent particles, one that has electric charge but has no spin and one that has spin but no charge. Fractionalization was discovered experimentally for electrons constrained to move in a plane in a semiconductor interface and exposed to strong magnetic field. Similar phenomenon had long been conjectured to occur naturally in materials. Recently several candidates were found. This project aims to develop theoretical and computational toolbox to discover and characterize fractionalized quantum phases in models and experimental materials. It will also study transformations that can occur among such states that lie outside the standard theory of phase transitions. The discovery of new quantum states of electronic matter in materials may lead to new technologies. The manipulation of some quantum states of electronic matter may lead to a new way to do computation, quantum computing, that would be potentially more powerful than existing computers.