Entanglement and emergence in quantum states of matter

物质量子态的纠缠和涌现

基本信息

批准号：
2022428
负责人：
Xiao-Gang Wen
金额：
$ 72万
依托单位：
Massachusetts Institute of Technology
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-08-15 至 2024-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2022428&HistoricalAwards=false
关键词：
Entanglement emergence quantum states matter

项目摘要

NONTECHNICAL SUMMARYThis award supports theoretical research and education that aims to use recently developed concepts for describing topological states of electrons in materials to gain insight into how strongly interacting systems of electrons organize themselves in electrically conducting states. There are many different kinds of materials in the world, such as metals, insulators, and semiconductors. These materials make electronic devices, such as cell phones, computers, TV's, and even the internet possible. To design electronic devices with desired functions, theories are needed to describe and to predict the properties of metals, insulators, and semiconductors.As the theoretical physicist Landau discovered, states of matter such as liquids and crystals can be organized through the symmetry transformations performed on a given state that leaves it unchanged. For example, a rotation of 90 degrees around a principle axis of a crystal of common salt, can rotate new atoms into positions that were originally occupied by the very same kind of atom, so the crystal appears unchanged. The concept of symmetry also allows magnetic and other states to be organized by similar considerations. In recent years, it has been discovered that ideas from topology, the branch of mathematics concerned with geometric properties that are unchanged by deformations, twisting, and stretching objects, bring insight into new possible phases of matter, called topological phases. Topological insulators are a common example. They are fundamentally different from ordinary insulators in that while the bulk does not conduct electricity, their surfaces do, as if they belonged to a metal.It is becoming understood that quantum entanglement is another underlying principle for materials, one which leads to a new class of quantum materials, also known as topological materials. Entanglement is a purely quantum property of a system that has no analog in our everyday experience. It reflects connections between the properties of a quantum system's parts, even if the parts become physically separated. The property is reflected in the structure of the many-electron state. The corresponding material theory -- the theory of topological order -- predicts a new class of insulators and semiconductors with new topological and quantum properties. These topological materials may play key roles in making quantum computers, just like silicon plays a key role in making commonly available conventional computers and cell phones of today.TECHNICAL SUMMARYThis award supports theoretical research and education that aims to use modern fundamental concepts developed for topological states of matter to gain insight into how strongly interacting systems of electrons organized in gapless states. Research over the last 30 years reveals that Landau's symmetry breaking theory only describes a small set of possible phases that matter can have. The phases of matter can be much richer than has ever imagined before. The concepts of topological order and symmetry protected trivial (SPT) order to describe those new types of quantum phases. After much research, a systematic classification understanding of all topological orders and SPT orders for both bosonic and fermionic systems, in 1-, 2-, and 3-dimensional spaces has emerged. The time is now ripe to attack the next big problem: a systematic understanding of strongly correlated gapless states. This award supports the PI's research to engage this problem.The PI takes the view that in general, an interacting system wants to be gapped, the most stable state. If an interacting system is gapless, the gapless state must be very special and highly organized, so that those gapless excitations can remain gapless even in the presence of interactions. This suggests that the general and systematic understanding of gapless quantumstates is possible. First, the low energy part of a gapless state may become several decoupled sectors, where the interactions between different sectors flow to zero in the infrared limit under renormalization group flow. This appears to happen quite generally, such as the sectors with different velocities in 1d gapless system become decoupled at low energies. Consequently, in the low energy limit, there are often emergent symmetries and higher symmetries. Since each decoupled low energy sector is not a full system, each sector byitself is often anomalous. A sector by itself may have a gravitational anomaly or higher symmetry anomaly. It is well known that an anomaly can affect low energy dynamics, in particular, it can protect the low energy excitations with the result that they are gapless in some cases. The "gaplessness" of each decoupled sector may be understood via its anomaly. This may enable a systematic understanding of strongly correlated gapless states. The strongly correlated gapless states should be much more complicated and much richer than strongly correlated gapped states. It may take some time to gain a fully systematic understanding of gapless states.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

非技术摘要这一奖项支持理论研究和教育，该奖项旨在使用最近开发的概念来描述材料中电子的拓扑状态，以深入了解电子相互作用的电子系统如何在电动导电状态中组织起来。世界上有许多不同种类的材料，例如金属，绝缘子和半导体。这些材料使电子设备（例如手机，计算机，电视甚至互联网）成为可能。要设计具有所需功能的电子设备，需要理论来描述和预测金属，绝缘体和半导体的特性。正如发现的理论物理学家Landau所发现的那样，液体和晶体等物质的状态可以通过在对称转换上进行组织。给定的状态，使其保持不变。例如，围绕普通盐晶体的原理轴旋转90度，可以将新的原子旋转成最初由同样的原子占据的位置，因此晶体显得不变。对称性的概念还允许通过类似的考虑来组织磁性和其他状态。近年来，已经发现，拓扑的思想，与几何特性有关的数学分支，这些数学特性不经过变形，扭曲和拉伸对象不变的几何特性，使人们对物质的新阶段（称为拓扑阶段）进行洞察力。拓扑绝缘子就是一个常见的例子。它们从根本上与普通绝缘子有所不同，因为虽然散装不进行电力，但它们的表面确实如此，好像它们属于金属一样。它已经众所周知，量子纠缠是材料的另一个基本原理，这会导致新的类别量子材料，也称为拓扑材料。纠缠是一个纯粹的量子特性，它的日常经验中没有类似物。它反映了量子系统零件的属性之间的连接，即使零件变得物理分离。该属性反映在许多电子状态的结构中。相应的材料理论 - 拓扑顺序的理论 - 预测具有新的拓扑和量子特性的新型绝缘体和半导体。这些拓扑材料可能在制造量子计算机中起关键作用，就像硅在制造当今的常规计算机和手机中起关键作用一样。技术摘要这一奖项支持理论研究和教育，旨在使用用于拓扑状态的现代基本概念的理论研究和教育物质以深入了解在无间隙状态中组织的电子系统的强烈相互作用。在过去的30年中，研究表明，兰道的对称性破坏理论只描述了可能具有的一小部分可能的阶段。物质的阶段可能比以往任何时候都要丰富。拓扑顺序和对称性受保护的琐事（SPT）的概念来描述那些新型的量子阶段。经过大量研究，已经出现了对骨气和费米斯系统的所有拓扑顺序和SPT订单的系统分类，并在1，2和3维空间中出现了。现在，攻击下一个大问题的时间已经成熟：对强烈相关的无间隙状态的系统理解。该奖项支持PI的研究来解决这个问题。如果相互作用的系统是无间隙的，则无间隙状态必须非常特殊且高度组织，以便即使在存在相互作用的情况下，这些无间隙激发也可以保持无间隙。这表明对无间隙量化的一般和系统理解是可能的。首先，无间隙状态的低能部分可能会变成几个解耦领域，在重新归一化组流量下，不同扇区之间的相互作用在红外极限中流到零。这似乎很普遍地发生，例如，在一维无间隙系统中具有不同速度的扇区在低能量下被脱钩。因此，在低能极限中，通常存在紧急的对称性和更高的对称性。由于每个分离的低能领域都不是一个完整的系统，因此每个部门毕必经自理通常都是异常的。一个部门本身可能具有重力异常或更高的对称异常。众所周知，异常会影响低能量动力学，特别是它可以保护低能激发，结果它们在某些情况下是无间隙的。每个解耦部门的“无间隙”可以通过其异常来理解。这可能使对密切相关的无间隙状态有系统的理解。与密切相关的间隙状态相比，密切相关的无间隙状态应更加复杂和丰富。该奖项反映了NSF的法定任务，可能需要一些时间才能获得完全系统的理解。该奖项被认为是值得通过基金会的知识分子优点和更广泛影响的评论标准来评估值得支持的。