Analytical and numerical studies of gapless fractionalized phases and topological phases and their transformations

无间隙分段相和拓扑相及其变换的分析和数值研究

• 批准号: 1619696
• 负责人: Olexei Motrunich
• 金额: $ 33万
• 依托单位: California Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-09-15 至 2020-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1619696&HistoricalAwards=false
• 关键词: Analytical; numerical; studies; gapless; fractionalized

NON-TECHNICAL SUMMARY:This award supports theoretical research and education on how electrons in solid materials organize themselves as a result of the interactions among them. The way the electrons organize corresponds to new quantum mechanical states of matter. Because of the interactions among the particles, the quantum mechanical state of electrons can appear to be composed of new kinds of particles with properties that may differ dramatically from the properties of the constituent electrons or atoms. The PI will study two archetypal examples: i) instances where the microscopic particles interlock in such a way that it appears as if the entire system was comprised of particles with properties that are fractions of the original constituent electrons or atoms, e.g. even though electrons are indivisible the system of electrons behaves as if it were comprised of particles having one-third of an electron's charge, and ii) instances where the microscopic particles form an unusual soup where the system behaves as if comprised of particles that have no mass, which consequently can transport their exotic properties over long distances. Similar states of matter can also occur in systems of very cold atoms trapped in a lattice formed by laser beams organize themselves as a result of the interactions among them.The quantum mechanical states in the first example underlie ideas of specific proposals for a new kind of computer that manipulates quantum mechanical states to do computation. The quantum mechanical states in the second example may hold insights into understanding many technologically important materials, most notably high-temperature superconductors. The electrons in superconductors self-organize into a quantum mechanical state that can carry electric current without dissipation. One of the main activities under this award will be to develop theoretical and computational toolboxes for the discovery and characterization of such quantum mechanical states in models and materials which may stimulate experimental inquiry. This project includes mentoring and training students and junior researchers at the frontier of condensed matter physics using a variety of advanced analytical and numerical techniques.TECHNICAL SUMMARY:This award supports theoretical research and education in theoretical condensed matter physics to investigate phases of quantum matter. Discoveries of quantum Hall fluids and also of numerous strongly correlated materials unveiled the richness of possible quantum many-body phenomena. The recent discovery of topological insulators together with advances in strongly correlated systems have even emboldened the community to contemplate complete classification of all quantum many-body phases. While great progress has been made for non-interacting or weakly-interacting electrons, properly describing strong interactions is crucial for any such larger endeavors, but this is also where the available tools are quite limited. Duality approaches have contributed significantly to understanding systems of strongly interacting bosons, in particular of fractionalized phases. Tractable models, which are either exactly solvable or numerically accessible, have provided another avenue for explorations of possible topological phases. The PI will continue to combine these approaches to construct explicit models that realize so-called symmetry-protected topological phases and to discover their fractionalized counterparts. The PI will study new phases that emerge as well as phase transformations involving them.While the goal of classifying gapped phases may be in sight, there is a vast poorly understood terrain of gapless states in strongly correlated systems, which are also of great experimental interest. Examples include heavy fermion materials near criticality, strange metal and pseudogap behaviors in high-temperature cuprate superconductors, composite fermi liquid state of the quantum Hall fluid at half-filling, and gapless spin liquid states in 2D organic materials. Recent advances in understanding three dimensional symmetry-protected topological phases have shed unexpected new light on this landscape: A long-standing problem of particle-hole symmetry of the composite fermi liquid state was related to physics of strongly correlated phases on surfaces of 3D topological insulators. At the same time, developments in Density Matrix Renormalization Group has allowed numerical studies of the composite fermi liquid with unprecedented detail. The PI will attack problems in this context. The PI will examine broader application of the fermionic dualities and investigate gapless fractionalized phases with emphasis on experimentally motivated questions for candidate spin liquid materials and sharp questions in controlled models. This project includes mentoring and training students and junior researchers at the frontier of condensed matter physics using a variety of advanced analytical and numerical techniques.

非技术总结：该奖项支持理论研究和教育，研究固体材料中的电子如何通过相互作用组织起来。电子的组织方式对应于物质的新量子力学状态。由于粒子之间的相互作用，电子的量子力学状态似乎是由新的粒子组成的，这些粒子的性质可能与组成电子或原子的性质截然不同。PI将研究两个原型示例：i）微观粒子以这样的方式互锁的情况，即看起来好像整个系统由具有原始组成电子或原子的分数的性质的粒子组成，例如，即使电子是不可分割的，电子系统的行为也好像它由具有电子电荷的三分之一的粒子组成，ii）微观粒子形成不寻常的汤的情况，其中系统表现得好像由没有质量的粒子组成，因此可以长距离传输它们的奇异特性。类似的物质状态也可以发生在由激光束形成的晶格中的非常冷的原子系统中，这些原子通过它们之间的相互作用而组织起来。第一个例子中的量子力学状态是关于一种新型计算机的具体建议的基础，这种计算机可以操纵量子力学状态进行计算。第二个例子中的量子力学状态可能有助于理解许多技术上重要的材料，特别是高温超导体。超导体中的电子自组织成量子力学状态，可以携带电流而不耗散。该奖项的主要活动之一将是开发理论和计算工具箱，用于发现和表征模型和材料中可能激发实验探究的量子力学状态。该项目包括使用各种先进的分析和数值技术指导和培训凝聚态物理前沿的学生和初级研究人员。技术概要：该奖项支持理论凝聚态物理的理论研究和教育，以研究量子物质的相。 量子霍尔流体和许多强关联材料的发现揭示了可能的量子多体现象的丰富性。 最近拓扑绝缘体的发现以及强关联系统的进展，甚至鼓励了社会考虑所有量子多体相的完整分类。 虽然对于非相互作用或弱相互作用的电子已经取得了很大的进展，但正确描述强相互作用对于任何此类更大的努力都至关重要，但这也是可用工具非常有限的地方。 对偶方法对理解强相互作用玻色子系统，特别是分数相系统有着重要的贡献。 易处理的模型，这是完全可解或数值访问，提供了另一种途径，探索可能的拓扑阶段。 PI将继续联合收割机这些方法来构建明确的模型，实现所谓的安全保护的拓扑阶段，并发现他们的分数对应。 PI将研究出现的新相以及涉及它们的相变。虽然对带隙相进行分类的目标可能已经在望，但在强关联系统中，存在着一个巨大的、人们知之甚少的无隙态领域，这也是非常有实验意义的。 例子包括临界附近的重费米子材料，高温铜酸盐超导体中的奇怪金属和赝能隙行为，半填充时量子霍尔流体的复合费米液态，以及2D有机材料中的无隙自旋液态。 最近的进展，在理解三维拓扑相的保护下，意外的新的光在这一景观：一个长期存在的问题，复合费米液体状态的粒子-空穴对称性是与物理学的强关联相表面的三维拓扑绝缘体。 与此同时，密度矩阵重整化群的发展使复合费米液体的数值研究具有前所未有的细节。 PI将在此背景下解决问题。 PI将研究费米对偶性的更广泛应用，并研究无间隙分馏相，重点是候选自旋液体材料的实验动机问题和受控模型中的尖锐问题。 该项目包括指导和培训学生和初级研究人员在凝聚态物理学的前沿使用各种先进的分析和数值技术。