Strongly Correlated Quantum Phases

该奖项支持强相互作用量子多体系统的理论研究和教育。 主要感兴趣的是窄带电子材料，其中电子相互作用可以具有显著的影响。 最引人注目的是半填充带材料，由于强相互作用而成为莫特绝缘体，与费米液体理论不一致。 虽然许多莫特绝缘体是有序的，但在几种新材料中，电子自旋在非常低的温度下仍保持液态。 这种自旋液体被认为具有许多奇特的性质。自旋液体有许多种类，有些是完全带隙的，具有隐藏的拓扑顺序，另一些则具有无隙的自旋携带激发。 在后一类中，最具挑战性的可能是？自旋玻色金属在动量空间中沿沿着表面表现出高度纠缠的无隙激发的相-大致类似于金属中的费米表面。 该项目的主要目标是通过分析和数值方法的结合--变分蒙特卡罗、规范理论、密度矩阵重整化群和玻色化--来攻击模型哈密顿量，从而发展对这种自旋玻色金属的理解。铜酸盐“奇怪金属”状态在最佳掺杂时的不寻常行为是第一个与费米液体理论惊人的背离之一，至今仍是个谜。把电子分裂成费米子的规范理论？spinon？和一个波斯语的“chargon”提供了为数不多的获得这种非费米液相的可用技术之一。 但是描述非费米液体需要将玻色子置于非超流的2D相。 最近的进展“玻色金属”相应允许访问全新类别的电子非费米液体。 PI将研究候选电子哈密顿量，这是可能表现出非费米液相使用数值和分析技术。采用准一维阶梯模型应该对系统地接近二维极限非常有帮助。该奖项支持凝聚态理论的高级研究生和博士后水平的培训。非技术总结该奖项支持专注于材料中物质的电子态的理论研究和教育，其中电子之间的强相互作用导致其运动的相关性，就像一个复杂的舞蹈。在每一个自然晶体中，都有一个舞蹈电子的奇异量子世界。每个水晶都有自己独特的舞蹈。在某些晶体中，电子的跳动模式是有组织的，有秩序的。在另一些内部，电子纠缠在量子运动的网络中。这个项目的一个目标是使用先进的概念，理论和计算方法来辨别这种电子舞蹈背后的“量子舞蹈”。 吸取的经验教训可能使未来拓扑量子计算机的设计基于物质的量子力学状态的操纵，以实现前所未有的性能为一些任务。固体的量子理论诞生于1930年，在描述许多材料的性质方面非常成功。 一个基本的前提是，忽略电子之间的相互作用是合理的，单独对待每个电子。 这一理论很好地解释了传统绝缘体、半导体和金属的许多性质。但在材料类的方法失败，有时在一个戏剧性的方式。 为这种强相互作用的电子系统开发一个新的理论框架是该领域的核心目标之一。在一类称为莫特绝缘体的新型材料中，电子完全被电子排斥力固定。 但是电子具有自旋的性质，使它们在粗略的意义上像小陀螺。莫特绝缘体中的自旋可以自由波动。 如果自旋在低温下保持无序排列，就会产生一种新的自旋液体状态，这种电子物质的状态被认为表现出一种奇异的新量子舞蹈。通过结合现代理论和数值技术，其中一些只是在过去几年才可能实现的，这是由于计算机速度的快速增长和新算法的开发，PI的目标是获得对自旋液体的理解-电子自旋纠缠态的复杂性，以及指导寻找有趣的新材料的能力。该项目为高级学生和博士后提供了宝贵的培训和研究经验。它还有助于未来电子设备和信息技术的知识基础。

TECHNICAL SUMMARYThis award supports theoretical research and education focused on strongly interacting quantum many-body systems. Of primary interest are narrow band electronic materials wherein electron interactions can have a dramatic impact. Most striking are half-filled band materials that are Mott insulators because of strong interactions, at odds with Fermi liquid theory. While many Mott insulators order, in several new materials the electron spins remain in a liquid state down to very low temperatures. Such spin-liquids are believed to harbor many exotic propertiesSpin liquids come in many varieties, some fully gapped with a hidden topological order, others with gapless spin-carrying excitations. Of the latter class, perhaps the most challenging are ?spin-Bose-metal? phases which exhibit highly entangled gapless excitations along surfaces in momentum space - loosely analogous to the Fermi surface in a metal. A main thrust of this project is to develop an understanding of such spin-Bose metals by attacking model Hamiltonians with a combination of analytical and numerical approaches - variational Monte Carlo, gauge theories, density-matrix-renormalization group, and Bosonization.The unusual behavior of the cuprate "strange metal" state at optimal doping was one of the first striking departures from Fermi liquid theory, and remains mysterious. Gauge theories, which split the electron into a Fermionic ?spinon? and a Bosonic "chargon"?, offer one of the few available techniques to access such non-Fermi liquid phases. But describing a non-Fermi liquid requires placing the Bosons into a non-superfluid 2D phase. Recent progress on "Bose-metal" phases should allow access to entirely new classes of electronic non-Fermi liquids. The PI will study candidate electron Hamiltonians which are likely to manifest non-Fermi liquid phases using both numerical and analytic techniques. Employing quasi-1D ladder models should be very helpful in systematically approaching the 2D limit.This award supports advanced graduate student and postdoc level training in condensed matter theory. NON-TECHNICAL SUMMARYThis award supports theoretical research and education focused on electronic states of matter in materials where strong interactions between electrons lead to correlations in their motions, rather like an intricate dance.Within each of nature's crystals is an exotic quantum world of dancing electrons. Each crystal has its own unique choreography. In some crystals the electron dancing patterns are structured and orderly. Within others the electrons are entangled in a web of quantum motion. One goal of this project is to use advanced concepts, and theoretical and computational methods to discern the "quantum choreography" that underlies such electron dances. Lessons learned may enable the design of a futuristic topological quantum computer based on the manipulation of quantum mechanical states of matter to achieve unprecedented performance for some tasks. The quantum theory of solids, born in 1930, has been extremely successful in describing the properties of many materials. A basic premise is that it is legitimate to ignore the interactions between the electrons, treating each one independently. This theory accounts well for many properties of conventional insulators, semiconductors and metals. But in classes of materials approach fails, sometimes in a dramatic way. Developing a new theoretical framework for such strongly interacting electron systems is one of the central goals of the field.In one novel class of materials called Mott insulators, the electrons are entirely immobilized by the electron repulsion. But electrons have the property of spin making them in a crude sense like tiny tops. The spins in Mott insulators are free to fluctuate. If the spins remain in a disorderly arrangement down to low temperatures, a novel spin-liquid state results, a state of electronic matter believed to manifest an exotic new quantum choreography.By combining an arsenal of modern theoretical and numerical techniques, some only possible in the past few years due to the rapid increase in computer speed and new algorithms that have been developed, the PI aims to gain understanding of spin-liquids - the intricacies of the entangled state of the electron's spins, and an ability to guide the search for interesting new materials. This project provides valuable training and research experience for advanced students and postdocs. It also contributes to the intellectual foundations of future electronic device and information technologies.