Highly Frustrated Interactions in Magnetic and Other Condensed Matter Systems

这是一个从理论上研究凝聚态系统的研究计划，特别是磁性系统，其中相关的微观自由度受到强烈竞争（受挫）相互作用的影响。四个广泛的问题的实验针对性，其中新现象产生的高挫折将被调查。******在大多数无无序凝聚态系统中，包括高度受挫的系统，低温状态显示出纳米长度尺度以上的本构原子、分子或磁矩（自旋）的均匀动力学。玻璃，表现出异质动力学（HD），是一个明显的例外。在最近的一项研究中，我们发现了一种罕见的无无序三维自旋模型，它显示了一种具有冻结和动态区域的状态，因此是高清的，并为这种状态创造了名称自旋泥。我们将揭示控制磁系统中自旋泥态形成的一般规则，首先关注自旋泥态在二维模型中的可能表现，并研究其空间和动力学性质以及量子效应的作用。******高度受挫的磁系统通常用规范理论来描述，这让人想起电磁学理论，人们很清楚，电场和磁场组成部分的边界条件起着基本的作用。基于这一观察结果，我们将研究边界条件如何影响纳米尺寸薄膜中高度受挫磁性材料的性质，例如目前正在进行的实验研究。最重要的是，我们将确定作用于描述经典和量子自旋冰薄膜的规范场的边界条件是什么。******像H2O和HF这样的极性小分子可以被封装在C60巴基球中，形成规则的晶体结构。目前人们对了解这种纳米限制系统的光谱以及它们可能表现出的集体（铁电）行为都很感兴趣。通过结合精确对角化、密度泛函理论和各种多体方法，我们将研究这些量子系统中这种集体行为的假定发展。******在大多数磁系统中，自旋通过所谓的双线性自旋-自旋交换相互作用，大多数高度受挫磁系统的理论研究都考虑了这样的设置。然而，真实的材料具有令人困惑的性质，其中预计存在显著的非双线性相互作用。我们将使用分析和数值方法的结合来探索这种相互作用是否确实可以解释这些系统的实验行为。******这项研究的结果将大大有助于我们对高度受挫凝聚态系统的全球理解，并可能导致令人兴奋的发现

This is a research proposal to theoretically study condensed matter systems, in particular magnetic ones, where the relevant microscopic degrees of freedom are subject to strongly competing (frustrated) interactions. Four broad problematics of experimental pertinence where novel phenomena arising from high frustration will be investigated.******In most disorder-free condensed matter systems, including highly frustrated ones, the low-temperature state displays homogeneous dynamics of the constitutive atoms, molecules or magnetic moments (spins) above a nanometer length scale. Glasses, which exhibit heterogeneous dynamics (HD), are a notable exception. In a recent study, we discovered a rare disorder-free three-dimensional spin model that displays a state with frozen and dynamic regions, thus HD, and coined the name spin slush for that state. We will uncover the general rules governing the formation of a spin slush in a magnetic system, focusing first on the possible manifestation of a spin slush state in two-dimensional models and study their spatial and dynamical properties along with the role of quantum effects.******Highly frustrated magnetic systems are often described by gauge theories reminiscent of the theory of electromagnetism for which it is well understood that boundary conditions on the components of the electric and magnetic fields play a fundamental role. Motivated by this observation, we will investigate how boundary conditions affect the properties of highly frustrated magnetic materials in nanometer size thin films such as those under current experimental investigation. Most importantly, we will determine what are the boundary conditions acting on the gauge fields that describe classical and quantum spin ice thin films. ******Small polar molecules such as H2O and HF can be encapsulated inside C60 buckyballs which form a regular crystal structure. There is current interest in understanding both the spectroscopy of such nanoconfined systems as well as the collective (ferroelectric) behaviour they may exhibit. By combining exact diagonalization, density functional theory and various many-body methods, we will investigate the putative development of such collective behaviour in these quantum systems.******In most magnetic systems, the spins interact via a so-called bilinear spin-spin exchange and most theoretical studies of highly frustrated magnetic systems consider such a setting. There are, however, real materials with puzzling properties where significant non-bilinear interactions are expected to exist. We will use a combination of analytical and numerical methods to explore whether such interactions can indeed explain the experimental behaviours of those systems.******Results from this research will significantly contribute to our global understanding of highly frustrated condensed matter systems and may lead to exciting discoveries.**