Quantum Magnetism in Low-Dimensional Materials

这项理论研究将研究材料的磁性，并为拉曼散射、中子散射和核磁共振（NMR）等实验表征工具提供基于模型的计算支持。大部分的研究依赖于两种应用于多体模型哈密顿量的计算方法。第一种是级数展开法，它是基于发展高阶微扰理论或幂级数展开热力学性质在一个合适的变量，如逆温度或耦合常数的比率。当这些展开参数很小且级数收敛时，直接求和可得到期望的结果。当膨胀参数变大时，采用Pade近似和相关的外推方法获得热力学量。已知这些方法在开发足够长的序列并且不跨越任何相位边界的情况下工作良好。与相变相关的奇异性质可以通过特殊开发的外推方案作为极限行为获得。第二种方法是基于随机级数展开技术的量子蒙特卡罗模拟。这是一种对配分函数高温展开中所有项求和的随机方法。使用最近开发的“操作员循环”更新，这种方法允许人们研究相当大的有限尺寸系统到低温。这些理论计算将用于研究新的和现有的磁性材料的性质。这些包括铜族高温超导材料和其他几种有机和无机材料。我们确定了一些最近合成的方形平面反铁磁材料和空间各向异性材料，它们表现出不同寻常的行为，其性质将得到解决。为了对真实材料的理解产生更大的影响，我们计划继续与电子结构理论家和实验组合作。这项研究的第二个目标是在强相互作用的多粒子系统中发展、建立或确认新的想法和概念。例如，涨落主导的一维物理是否可以延续到高维系统的问题将被解决。另一个有趣的问题是是否存在二维自旋模型，具有奇异相和可能的分数自旋激发。具体的模型，其性质将计算，进行了讨论。第三个目标是进一步发展和扩展计算方法本身，以便它们可以用于更广泛的模型类别和更大类别的实验特性。我们将关注有限温度下磁系统的动力学性质，这对于定量理解中子散射和核磁共振结果是最重要的。这些计算研究为学生和博士后提供了很好的训练。这项理论研究将研究材料的磁性，并为拉曼散射、中子散射和核磁共振（NMR）等实验表征工具提供基于模型的计算支持。大部分的研究依赖于两种应用于多体模型哈密顿量的计算方法。这些是级数展开技术和量子蒙特卡罗方法。这些学习为学生提供了很好的训练

This theoretical research will study magnetic properties of materials and provide model-based computational support for experimental characterization tools such as Raman scattering, neutron scattering and nuclear magnetic resonance (NMR). The bulk of the study relies on two types of computational methods applied to many-body model Hamiltonians.The first is the series expansion method, which is based on developing high order perturbation theory or power-series expansions for thermodynamic properties in a suitable variable such as inverse temperature or ratio of coupling constants. When these expansion parameters are small and the series are convergent, a direct summation provides the desired answer. Pade approximants and related extrapolation methods are used to obtain thermodynamic quantities when the expansion parameters become large. These methods are known to work well provided one develops a long enough series and does not cross any phase boundaries. The singular properties associated with the phase transitions can be obtained as a limiting behavior from specially developed extrapolation schemes.The second method is quantum Monte Carlo simulations based on the stochastic series expansion technique. This is a stochastic method to sum up all the terms in a high temperature expansion of the partition function. Using recently developed "operator loop" updates, this method allows one to study fairly large finite-size systems down to low temperatures. These theoretical calculations will be used to study properties of novel and existing magnetic materials. These include the cuprate family of high temperature superconducting materials and several other organic and inorganic materials. We identify a number of recently synthesized square-planar antiferromagnetic materials and spatially anisotropic materials exhibiting unusual behavior, whose properties will be addressed. In order to have a greater impact on the understanding of real materials, we plan to continue our collaborations with electronic structure theorists and experimental groups.A second objective of this research is to develop, establish or confirm new ideas and concepts in strongly interacting many-particle systems. For example, the question of whether fluctuation dominated one-dimensional physics can carry over to higher dimensional systems will be addressed. Another question of interest is whether there exist two-dimensional spin models, with exotic phases and possibly fractional spin excitations. Specific models, whose properties will be calculated, are discussed.A third objective is to further develop and extend the computational methods themselves so that they can be used for a wider class of models and for a larger class of experimental properties. We will focus on dynamical properties of magnetic systems at finite temperatures, which would be most important in quantitatively understanding neutron scattering and NMR results. These computational studies provide excellent training for students and postdoctoral associates.%%%This theoretical research will study magnetic properties of materials and provide model-based computational support for experimental characterization tools such as Raman scattering, neutron scattering and nuclear magnetic resonance (NMR). The bulk of the study relies on two types of computational methods applied to many-body model Hamiltonians. These are series-expansion techniques and quantum Monte Carlo methods. These studies provide excellent training for students.***