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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.

非技术摘要该奖项支持理论研究和教育，旨在使用最近开发的概念来描述材料中电子的拓扑状态，以深入了解电子的强相互作用系统如何在导电状态下组织自身。世界上有许多不同种类的材料，例如金属、绝缘体和半导体。这些材料使手机、电脑、电视甚至互联网等电子设备成为可能。为了设计具有所需功能的电子设备，需要用理论来描述和预测金属、绝缘体和半导体的特性。正如理论物理学家朗道所发现的那样，液体和晶体等物质的状态可以通过在给定状态上进行对称变换来组织，而保持状态不变。例如，围绕食盐晶体的主轴旋转 90 度，可以将新原子旋转到最初由同类原子占据的位置，因此晶体看起来没有变化。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，人们发现，拓扑学（涉及物体变形、扭曲和拉伸不会改变的几何特性的数学分支）的思想可以深入了解物质的新的可能相，称为拓扑相。拓扑绝缘体是一个常见的例子。它们与普通绝缘体有根本的不同，因为虽然其本体不导电，但它们的表面却导电，就好像它们属于金属一样。人们逐渐理解，量子纠缠是材料的另一个基本原理，它催生了一类新的量子材料，也称为拓扑材料。纠缠是系统的纯粹量子特性，在我们的日常经验中没有类似物。它反映了量子系统各部分属性之间的联系，即使这些部分在物理上是分离的。该性质反映在多电子态的结构中。相应的材料理论——拓扑序理论——预测了具有新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发挥关键作用，就像硅在当今普及的传统计算机和手机中发挥关键作用一样。技术摘要该奖项支持理论研究和教育，旨在利用为物质拓扑态开发的现代基本概念来深入了解在无间隙状态下组织的电子系统的强相互作用。过去 30 年的研究表明，朗道的对称性破缺理论仅描述了物质可能具有的一小部分可能的相。物质的相态可能比以前想象的要丰富得多。拓扑序和对称保护平凡（SPT）序的概念来描述这些新型量子相。经过大量研究，对 1 维、2 维和 3 维空间中的玻色子和费米子系统的所有拓扑级和 SPT 级的系统分类理解已经出现。现在解决下一个大问题的时机已经成熟：对强相关无间隙态的系统理解。该奖项支持 PI 解决这一问题的研究。PI 认为，一般来说，相互作用的系统希望处于有间隙的状态，即最稳定的状态。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化，以便即使存在相互作用，这些无间隙激发也可以保持无间隙。这表明对无带隙量子态的普遍和系统的理解是可能的。首先，无间隙态的低能部分可能会变成几个解耦扇区，其中不同扇区之间的相互作用在重正化群流下在红外极限内流向零。这似乎很普遍地发生，例如一维无间隙系统中具有不同速度的扇区在低能量下变得解耦。因此，在低能量极限下，经常会出现涌现对称性和更高的对称性。由于每个解耦的低能耗部门都不是一个完整的系统，因此每个部门本身通常都是异常的。一个扇区本身可能存在重力异常或更高的对称性异常。众所周知，异常会影响低能动力学，特别是它可以保护低能激发，从而在某些情况下它们是无间隙的。每个解耦扇区的“无间隙”可以通过其异常来理解。这可以实现对强相关无间隙状态的系统理解。强相关的无间隙状态应该比强相关的有间隙状态更加复杂和丰富。可能需要一些时间才能对无间隙状态获得完全系统的了解。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。