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

新颖的碎裂相和异常相变的分析和数值研究

• 批准号: 1206096
• 负责人: Olexei Motrunich
• 金额: $ 30.73万
• 依托单位: California Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2016-02-29
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1206096&HistoricalAwards=false
• 关键词: Analytical; numerical; studies; novel; fractionalized

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.

该奖项支持在受挫折的量子磁体中分馏自旋液相的理论研究和教育。 最近发现的几种候选自旋液体材料的自旋驻留在二维和三维晶格上的刺激了这项研究。 PI的目的是扩大现有的工具箱波函数的分数阶段使用部分子的方法。 在这种方法中，微观自旋或玻色子算子被分裂成辅助类夸克场，这些场在平均场中被取消限制，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Gutzwiller投影的从费米子态，PI还将使用投影的Schwinger玻色子波函数，这些波函数是磁有序相附近的强候选者，以及从Majorana从费米子方法中激发的新波函数，这些方法可以进一步丰富具有无隙自旋子的状态池。 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。在一个单独的推力中，PI将致力于更好地理解无间隙的分数相，其中涌现的规范场也是无间隙的，这是一些最具挑战性的情况下，分析方法不受完全控制。 PI将建立在一个例子激子玻色液相模型与纯环交换，其中部分子规范的方法可以完成，也与非部分子的方法进行比较。 该研究将解决激子玻色液体理论中的一些悬而未决的问题，并将使用这些来了解无隙部分规范系统。PI还将探索统计力学问题中不寻常的相变与拓扑项，结合分析对偶方法和数值蒙特卡罗技术在一个强大的方式。 重点将放在具有相互统计相互作用的粒子的模型上。 这种模型出现在拓扑相及其相变的研究中，也出现在受抑量子反铁磁体的有效场论中。 该研究将有助于理解最近非常感兴趣的非常规量子相变。非技术总结该奖项支持理论研究和教育，重点关注表现出一种分馏现象的物质的不寻常量子态。从某种意义上说，电子就像微小的旋转陀螺，用自旋这个术语来量化。它们还携带一个单位的电荷。当电子看起来像是被分裂成两个独立的粒子时，就会产生分形，一个粒子带电荷但没有自旋，另一个粒子带自旋但没有电荷。实验发现，在强磁场作用下，半导体界面中的电子在平面内运动时会发生分形现象。类似的现象早已被证实在材料中自然发生。 最近发现了几个候选者。本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数量子相。 它还将研究相变的标准理论之外的状态之间可能发生的转换。材料中电子物质新量子态的发现可能会导致新技术的出现。对电子物质的某些量子态的操纵可能会导致一种新的计算方式，即量子计算，它可能比现有的计算机更强大。