Harnessing disorder to tune, tailor and design classical and quantum spin liquids

纠缠支撑了量子力学的许多定义的非经典性质，而长程纠缠会产生奇异的现象，如分数量子数和突然出现的拓扑激发。下一代量子技术将依赖于我们对相干和纠缠的理解和利用，而这一提议直接解决了这些问题。大量长程纠缠相的例子是量子自旋液体--量子磁铁的状态，其中电子自旋驻留在无限多无序的类液体微态的宏观叠加中。受挫的焦绿石磁体通常在最低温度下都表现出类似液体的短程关联，因此是研究经典和量子自旋液体行为的理想候选材料。任何形式的无序的存在--波动、应变、结构缺陷--通常被认为是一种滋扰，有可能掩盖或破坏备受追捧的自旋液体相。然而，最近的研究也表明，结构无序的存在有时可以稳定经典和量子自旋液体，甚至可以导致新的磁自由度、拓扑自旋玻璃的形成和全新量子自旋液体的形成。受这些结果的启发，我们在这里把无序作为一种资源来定制、调整和控制自旋液体行为和量子纠缠。具体地说，我们建议通过掺杂在焦绿石材料中引入可控的结构无序，并利用单晶扩散中子散射来确定缺陷结构。这些测量的结果将使我们能够开发理论模型和模拟，以了解缺陷如何改变离子的磁性和它们的集体行为。除了用于量子自旋液体行为的候选材料外，我们还将在所谓的“经典”状态下研究相关材料，在这种状态下，没有无序的性质被更好地理解，建模和模拟能力通常更强；在这样做的过程中，我们将为更具挑战性的量子状态的分析提供洞察和支持。在我们协调一致的理论-实验方法中，我们希望从建模中获得的洞察力将反馈到决定进一步增长哪些样本和执行哪些测量来验证我们的预测，范围从热力学测量到使用极化中子的动力结构因素。我们将研究以下问题：量子自旋液体相的稳定性；无序引入的有效横场对量子涨落的促进；出射激发的散射和陷阱，以及一般的局域化和玻璃化问题，以响应结构扭曲所产生的无序。我们的首要目标是研究拓扑、玻璃性和流动性之间的关系，并获得量子自旋液体中长程纠缠的明确证据。

Entanglement underpins many of the defining non-classical properties of quantum mechanics, and long-range entanglement engenders exotic phenomena such as fractional quantum numbers and emergent topological excitations. The next generation quantum technologies will rely on our understanding and exploitation of coherence and entanglement, and this proposal directly tackles these issues. Exemplars of massive long-range entangled phases are quantum spin liquids -- states of quantum magnets in which electronic spins reside in macroscopic superpositions of infinitely many disordered, liquid-like microstates. Frustrated pyrochlore magnets often exhibit liquid-like short-range correlations down to the lowest temperatures and are therefore ideal candidate materials to look for classical and quantum spin liquid behaviour. The presence of disorder in any of its forms -- fluctuations, strain, structural defects -- is usually regarded as a nuisance that has the potential to obscure or disrupt the sought-after spin liquid phase. However, it has also been recently shown that the presence of structural disorder can sometimes stabilise classical and quantum spin liquids, and it can even lead to new magnetic degrees of freedom, the formation of topological spin glasses and the formation of entirely novel quantum spin liquids. Inspired by these results, we here take the view of disorder as a resource to tailor, tune and control spin liquid behaviour and quantum entanglement. Specifically, we propose to introduce structural disorder in pyrochlore materials in a controlled manner via doping, and to determine the defect structures using single-crystal diffuse neutron scattering. The results from these measurements will allow us to develop theoretical models and simulations to understand how the defects change the magnetic properties of the ions and their collective behaviour. In parallel to candidate materials for quantum spin liquid behaviour, we will also study related materials in the so-called `classical' regime, where the properties without disorder are better understood and where modelling and simulation capabilities are generally greater; in doing this we shall provide insight and support to the analysis of the more challenging quantum regime. In our concerted theory-experiment approach, we expect the insight from modelling to feed back into deciding which further samples to grow and which measurements to perform to test our predictions, ranging from thermodynamic measurements to dynamical structure factors using polarized neutrons. We will investigate questions about the stability of quantum spin liquid phases; the promotion of quantum fluctuation due to effective transverse fields introduced by disorder; the scattering and trapping of emergent excitations, and in general questions about localisation and glassiness, in response to the disorder produced by structural distortions. Our overarching aim is to investigate the relationship between topology, glassiness and liquidity, and to obtain unambiguous evidence for long-range entanglement in quantum spin liquids.