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

非技术概述：该奖项支持关于固体材料中的电子如何由于它们之间的相互作用而自我组织的理论研究和教育。电子的组织方式与物质的新量子力学状态相对应。由于粒子之间的相互作用，电子的量子力学状态可能看起来是由新类型的粒子组成的，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将研究两个典型的例子：i)微观粒子以一种方式相互交错，似乎整个系统是由具有原始组成电子或原子的一部分性质的粒子组成的，例如，即使电子是不可分割的，电子系统的行为就像它是由具有三分之一电子电荷的粒子组成的，以及ii)微观粒子形成不寻常的汤的情况，其中系统的行为就像是由没有质量的粒子组成，因此可以长距离传输它们的奇异性质。类似的物质状态也可以出现在被困在由激光形成的晶格中的非常冷的原子系统中，这是它们之间相互作用的结果。第一个例子中的量子力学状态是操纵量子力学状态进行计算的新型计算机的具体建议的想法的基础。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，最著名的是高温超导体。超导体中的电子自组织成一种量子力学状态，可以携带电流而不耗散。该奖项下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的这种量子力学状态，这可能会刺激实验研究。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。技术摘要：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。量子霍尔流体和大量强关联材料的发现揭示了可能存在的量子多体现象的丰富性。最近拓扑绝缘体的发现，加上强关联系统的进步，甚至鼓励了社区考虑对所有量子多体相进行完整的分类。虽然在不相互作用或弱相互作用的电子方面已经取得了很大的进展，但适当地描述强相互作用对于任何这样的更大的努力都是至关重要的，但这也是可用的工具相当有限的地方。二元性方法对理解强相互作用玻色子系统，特别是分化相的系统做出了重大贡献。易处理的模型，要么是精确可解的，要么是数值可达的，为探索可能的拓扑阶段提供了另一种途径。PI将继续结合这些方法来构建显式模型，以实现所谓的对称保护的拓扑相，并发现其细分的对应物。PI将研究出现的新相以及涉及它们的相变。虽然对有间隙相进行分类的目标可能已经指日可待，但在强关联系统中有一个广袤而鲜为人知的无间隙状态地形，这也是非常有实验意义的。例子包括接近临界的重费米子材料，高温铜酸盐超导体中的奇异金属和伪隙行为，半填充态量子霍尔流体的复合费米液体状态，以及二维有机材料中的无间隙自旋液体状态。在理解三维对称性保护的拓扑相方面的最新进展为这一图景提供了意想不到的新线索：复合费米液态的粒子-空穴对称性的长期问题与3D拓扑绝缘体表面的强关联相的物理有关。同时，密度矩阵重整化群的发展使得对复合费米液体的数值研究具有了前所未有的细节。私人投资公司将在这种情况下解决问题。PI将研究费米子对偶的更广泛的应用，并研究无缝隙细分相，重点是候选自旋液体材料的实验激励问题和受控模型中的尖锐问题。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。

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.