Emergence: from nanomagnets to quantum spin liquids

出现：从纳米磁体到量子自旋液体

• 批准号: RGPIN-2022-05240
• 负责人: Ramachandran, Ganesh
• 金额: $ 2.04万
• 依托单位: Brock University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=762558
• 关键词: Emergence; nanomagnets; quantum; spin; liquids

A collection of entities, at a certain scale and complexity, can acquire a new 'emergent' identity. A classic example is the raindrop, a collection of 1020 water molecules at room temperature and pressure. The raindrop is completely unlike a water molecule. It even obeys a different set of physical laws, e.g., its shape is determined by surface tension, a concept that has no meaning at the molecular level. We say that the raindrop has 'emerged' as an independent object. As emergence is highly nonlinear, it cannot usually be calculated from first principles. For example, starting with knowledge of water molecules, it is impossible to predict the shape of a raindrop. However, recent work from my group shows that such predictions can be made in a large class of quantum magnets. They follow an 'emergence principle': at low energies, the quantum magnet resembles a single particle that moves according to the laws of quantum mechanics. The particle moves on an abstract space that can often be determined from simple geometric arguments. For example, an XY dimer (a simple magnet with two spins) emerges as a particle that moves on a circle. The energy levels of the magnet are indistinguishable from that of the particle. I propose to build on this idea to understand the mechanisms that underlie emergence and to engineer desirable emergent properties. My first objective is to find novel emergent properties in nanomagnets. At low temperatures, these small magnets resemble simple single-particle problems. The particle's motion can be affected by quantum effects such as Berry phase and interference. I hope to establish nanomagnets as a platform to study quantum dynamics, exploring ideas such as ergodicity, thermalization and quantum chaos. My second objective is to study localization. Recent studies from my group have demonstrated 'quantum indecision' where a low-energy particle freezes at a crossroads, unable to pick a direction. This is seen in the emergent physics of certain quantum magnets with the magnet effectively freezing into an ordered configuration. This idea has only been demonstrated in small model systems. I propose to extend it to larger systems that are experimentally realizable, e.g., in metals where electrons can be thought to move along Fermi surfaces. The third goal of my research programme is to study quantum spin liquids, emergent states of magnets where spins do not order. They have been described using gauge theory, a concept that originates from electromagnetism. I seek to address two broad open questions - how do spins settle into an unordered state? What gives rise to gauge structure? I propose to study candidate spin liquids that are built from triangular and tetrahedral motifs. Using the emergence principle at the level of each motif, I propose to construct field theory descriptions. This can reveal the approach to emergence, tracking the physics of the magnet as its energy is lowered.

一定规模和复杂性的实体集合可以获得新的“新兴”身份。一个经典的例子是雨滴，这是在室温和压力下的1020个水分子的集合。雨滴完全不同于水分子。它甚至遵守一组不同的物理定律，例如，其形状是由表面张力决定的，表面张力在分子水平上没有意义。我们说雨滴已经“出现”为独立对象。 由于出现是高度非线性的，因此通常无法根据第一原理进行计算。例如，从了解水分子的知识开始，无法预测雨滴的形状。但是，我小组的最新工作表明，可以在大量的量子磁铁中做出这样的预测。它们遵循“出现原理”：在低能时，量子磁铁类似于根据量子力学定律移动的单个粒子。粒子在抽象空间上移动，通常可以从简单的几何参数确定。例如，XY二聚体（带有两个自旋的简单磁铁）作为在圆上移动的粒子出现。磁铁的能级与粒子的能级没有区别。我建议以这一想法为基础，以了解出现的基础和工程师期望的新兴特性的机制。 我的第一个目标是在纳米磁体中找到新的新兴特性。在低温下，这些小磁铁类似于简单的单粒子问题。粒子的运动可能会受到量子效应（例如浆果相和干扰）的影响。我希望将纳米磁铁建立为研究量子动态的平台，探索诸如奇迹，热化和量子混乱等思想。 我的第二个目标是研究本地化。我小组的最新研究表明，低能粒子在十字路口冻结，无法选择方向。在某些量子磁体的新兴物理学中可以看到这一点，并有效地将其冻结成有序的配置。这个想法仅在小型模型系统中得到了证明。我建议将其扩展到在实验上可实现的较大系统，例如，在可以认为电子沿费米表面移动的金属中。 我的研究计划的第三个目标是研究量子旋转液体，即旋转未订购的磁铁的新兴状态。它们已经使用量规理论描述了它们，该概念源自电磁学。我试图解决两个广泛的公开问题 - 旋转如何安顿在一个无序的状态下？是什么引起量规结构？我建议研究由三角形和四面体基序建造的候选旋转液体。我建议使用每个基序的出现原理，提议构建现场理论描述。这可以揭示出出现的方法，并随着磁铁的降低而跟踪磁铁的物理。