Interpretations of ground-state symmetry breaking and strong correlation in wavefunction and density functional theories

Strong correlations within a symmetry-unbroken ground-state wavefunction can show up in approximate density functional theory as symmetry-broken spin-densities or total densities, which are sometimes observable. They can arise from soft modes of fluctuations (sometimes collective excitations) such as spin-density or charge-density waves at non-zero wavevector. In this sense, an approximate density functional for exchange and correlation that breaks symmetry can be more revealing (albeit less accurate) than an exact functional that does not. The examples discussed here include the stretched H2 molecule, antiferromagnetic solids, and the static charge-density wave/Wigner crystal phase of a low-density jellium. Time-dependent density functional theory is used to show quantitatively that the static charge density wave is a soft plasmon. More precisely, the frequency of a related density fluctuation drops to zero, as found from the frequency moments of the spectral function, calculated from a recent constraint-based wavevector- and frequency-dependent jellium exchange-correlation kernel.

This record contains all raw data used in this project. The second version contains better-converged data for the frequency moments. The parameters used to generate this data are included in a text file. The third version includes third moment sum rule data that is more stable (a typo in the spline interpolation was rectified, see the Gitlab commit record for more detailed information), as well as expanded correlation energy per electron data. The MCP07 analytic continuation to imaginary frequencies is also more correctly treated in this new data set.

未破缺对称性的基态波函数内的强关联效应，在近似密度泛函理论（density functional theory）中会表现为破缺对称性的自旋密度或总密度，这类现象有时可被观测到。此类效应可源于非零波矢下的涨落软模（有时为集体激发），例如自旋密度波或电荷密度波。就此而言，具备对称性破缺特性的近似交换-关联泛函，相较于无对称性破缺的精确泛函，往往能提供更多物理洞察（尽管其精度稍低）。本文讨论的案例包括拉伸态氢分子（H₂）、反铁磁固体，以及低密度均匀电子气（jellium）的静态电荷密度波/维格纳晶体相。研究采用含时密度泛函理论（time-dependent density functional theory）定量证明了，静态电荷密度波属于一种软等离激元。更准确地说，相关密度涨落的频率会降至零——这一结论来自对谱函数频率矩的分析，而谱函数的计算基于近期提出的、受约束的波矢与频率依赖型均匀电子气交换-关联核。

本数据集包含本项目所用的全部原始数据。第二版数据集包含了收敛性更优的频率矩数据，生成该数据所用的参数已收录于配套文本文件中。第三版新增了稳定性更优的三阶矩求和规则数据（修正了样条插值中的一处笔误，详细信息可参阅Gitlab提交记录），同时补充了扩展后的单电子关联能数据集。本新版数据集还对MCP07解析延拓至虚频的处理流程进行了更精准的修正。