论文标题
在预算中探索希尔伯特空间：新颖的基准集和用于测试强相关状态的电子结构方法的性能指标
Exploring Hilbert space on a budget: Novel benchmark set and performance metric for testing electronic structure methods in the regime of strong correlation
论文作者
论文摘要
这项工作探讨了经典电子结构方法有效表示（压缩）完整配置相互作用（FCI）波函数的信息内容的能力。我们引入了一个具有不同维度和独特电子结构的四个氢模型系统的基准集：一维链，一个1D环，2D三角形晶格和3D封闭式金字塔。为了评估计算方法产生准确和紧凑的波函数的能力，我们介绍了精度量，该度量是测量实现目标能量误差所需的变异参数数量的度量。 Using this metric and the hydrogen models, we examine the performance of three classical deterministic methods: i) selected configuration interaction (sCI) realized both via an a posteriori and variational selection of the most important determinants, ii) rank-reduced FCI, obtained by an a posteriori singular value decomposition of the FCI tensor (SVD-FCI), and iii) the matrix product state representation obtained via the密度基质重归其化组（DMRG）。我们发现，DMRG通常为所有系统提供最有效的波函数表示，尤其是在具有局部基础的1D链中。对于2D和3D系统，所有方法都以离域的基础表现最佳，并且SCI的效率更接近DMRG，而前者的具有强度和准确性量的大约是强相关性方案的两倍。与SCI相比，通常发现SVD-FCI方案需要稍大的参数才能达到相同的能量准确性。
This work explores the ability of classical electronic structure methods to efficiently represent (compress) the information content of full configuration interaction (FCI) wave functions. We introduce a benchmark set of four hydrogen model systems of different dimensionality and distinctive electronic structures: a 1D chain, a 1D ring, a 2D triangular lattice, and a 3D close-packed pyramid. To assess the ability of a computational method to produce accurate and compact wave functions, we introduce the accuracy volume, a metric that measures the number of variational parameters necessary to achieve a target energy error. Using this metric and the hydrogen models, we examine the performance of three classical deterministic methods: i) selected configuration interaction (sCI) realized both via an a posteriori and variational selection of the most important determinants, ii) rank-reduced FCI, obtained by an a posteriori singular value decomposition of the FCI tensor (SVD-FCI), and iii) the matrix product state representation obtained via the density matrix renormalization group (DMRG). We find that DMRG generally gives the most efficient wave function representation for all systems, particularly in the 1D chain with a localized basis. For the 2D and 3D systems, all methods perform best with a delocalized basis, and the efficiency of sCI is closer to that of DMRG, with the former having and accuracy volume approximately twice as large in the strong correlation regime. Compared to sCI, the SVD-FCI scheme is generally found to require a slightly larger number of parameters to achieve the same energy accuracy.
