Abstract We present UNDI, an open-source program to analyse the time dependent spin polarization of an isolated muon interacting with the surrounding nuclear magnetic dipoles in the context of standard muon spin rotation and relaxation spectroscopy experiments. The code can perform both exact and approximated estimates of the muon polarization function in presence of external fields and electric field gradients on the nuclei surrounding the muon. We show that this tool, combined to ab initio estimations of the electric field gradient at the nuclei interacting with the muon, can become a valuable complement to supercell based identifications of muon sites in crystals when large nuclear magnetic moments are present in the sample. In addition, it allows to properly investigate physical properties influenced by the presence of a non-negligible electric field gradient such as avoided level crossing resonance, nature of the ground state, disentanglement of electronic and nuclear magnetic moments or charge ordered states. The efficiency and effectiveness of this method is shown along the lines of three realistic examples. Program summary Program Title: UNDI CPC Library link to program files: http://dx.doi.org/10.17632/grp8njy6gz.1 Developer’s respository link: https://github.com/bonfus/undi Code Ocean capsule: https://codeocean.com/capsule/8365303 Licensing provisions: GPLv3 Programming language: Python Nature of problem: To simplify and potentially automate the analysis of the nuclear contribution to muon polarization functions in crystalline materials. Solution method: A python library that provides a set of tools to efficiently solve the spin Hamiltonian describing the interaction between the muon and its neighbouring nuclei. The code provides the time development of the spin polarization of the muon subject to external fields and accounts for quadrupolar interactions at the nuclear sites. The solution is sought at quantum level accuracy and Hilbert spaces with dimension up to one million can be handled, thus providing accurate results for all standard experimental conditions.

中文翻译：

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UNDI：一个用于模拟固体中介子核相互作用的开源库

摘要 我们提出了 UNDI，这是一个开源程序，用于在标准 μ 子自旋旋转和弛豫光谱实验的背景下分析与周围核磁偶极子相互作用的孤立 μ 子的时间相关自旋极化。在存在外部场和μ子周围核上的电场梯度的情况下，该代码可以执行μ子极化函数的精确估计和近似估计。我们表明，当样品中存在大核磁矩时，该工具与对与 μ 子相互作用的核处的电场梯度的从头估计，可以成为对基于超晶胞鉴定晶体中 μ 子位点的有价值的补充。此外，它允许正确研究受存在不可忽略的电场梯度影响的物理特性，例如避免的水平交叉共振、基态的性质、电子和核磁矩的解缠结或电荷有序态。该方法的效率和有效性通过三个实际例子来展示。程序概要 程序名称：UNDI CPC 库程序文件链接：http://dx.doi.org/10.17632/grp8njy6gz.1 开发者资源库链接：https://github.com/bonfus/undi 代码海洋胶囊：https:// /codeocean.com/capsule/8365303 许可条款：GPLv3 编程语言：Python 问题性质：简化和潜在自动化对晶体材料中介子极化函数的核贡献分析。解决方法：一个python库，它提供了一组工具来有效地解决描述μ子与其相邻核之间相互作用的自旋哈密顿量。该代码提供了受外部场影响的 μ 子自旋极化的时间发展，并解释了核位点的四极相互作用。该解决方案是在量子级精度上寻求的，并且可以处理维度高达一百万的希尔伯特空间，从而为所有标准实验条件提供准确的结果。