使用切比雪夫投影算子的快速收敛量子蒙特卡罗方法
Rapidly convergent quantum Monte Carlo using a Chebyshev projector
AI总结：
本文提出基于度量树的激发搜索、对称性筛选和切比雪夫墙投影算子等算法改进，显著加速MR-CCMC及各类投影QMC方法的收敛，并在铍、碳二聚体上完成基准验证。
摘要：
多参考耦合簇蒙特卡罗（MR-CCMC）算法是一种基于行列式的量子蒙特卡罗（QMC）算法，在概念上与全组态相互作用量子蒙特卡罗（FCIQMC）相似。已有研究表明，该算法能够在保持多项式标度的同时，对静态相关和动态相关提供均衡的处理，但将其应用于具有显著强相关的大型体系此前仍不切实际。本文记录了近期取得的多项算法进展，这些进展能够实现快速收敛，并为多参考问题提供一种更具黑箱特性的处理方式。这些进展包括：一种对数标度的、基于度量树的激发接受算法，用于在所需激发级别上搜索与参考空间相连的行列式；以及一种针对参考空间的对称性筛选程序。我们表明，对于中等规模的参考空间，新的搜索算法使一次 MR-CCMC 迭代大约加速 8 倍，而对称性筛选程序在几乎不损失精度的情况下减少了活跃参考空间行列式的数量。我们还引入了一种近似墙投影算子的随机实现，该墙投影算子是指数投影算子在无穷虚时间极限下的结果，其实现方式是将墙函数在切比雪夫多项式中进行截断展开。值得注意的是，这种墙-切比雪夫投影算子可用于加速任何基于投影算子的 QMC 算法。我们表明，该投影算子只需显著更少的哈密顿量作用次数即可达到相同的统计收敛效果。我们以铍二聚体和碳二聚体为基准体系，使用 initiator FCIQMC 和 MR-CCMC 以及最高达 cc-pVQZ 质量的基组，对这些加速方法进行了基准测试。
英文摘要：
The multi-reference coupled-cluster Monte Carlo (MR-CCMC) algorithm is a determinant-based quantum Monte Carlo (QMC) algorithm that is conceptually similar to Full Configuration Interaction QMC (FCIQMC). It has been shown to offer a balanced treatment of both static and dynamic correlation while retaining polynomial scaling, although application to large systems with significant strong correlation remained impractical. In this paper, we document recent algorithmic advances that enable rapid convergence and a more black-box approach to the multi-reference problem. These include a logarithmically scaling metric-tree based excitation acceptance algorithm to search for determinants connected to the reference space at the desired excitation level and a symmetry-screening procedure for the reference space. We show that, for moderately sized reference spaces, the new search algorithm brings about an approximately 8-fold acceleration of one MR-CCMC iteration, while the symmetry screening procedure reduces the number of active reference space determinants at essentially no loss of accuracy. We also introduce a stochastic implementation of an approximate wall projector, which is the infinite imaginary time limit of the exponential projector, using a truncated expansion of the wall function in Chebyshev polynomials. Notably, this wall-Chebyshev projector can be used to accelerate any projector-based QMC algorithm. We show that it requires significantly fewer applications of the Hamiltonian to achieve the same statistical convergence. We benchmark these acceleration methods on the beryllium and carbon dimers, using initiator FCIQMC and MR-CCMC with basis sets up to cc-pVQZ quality.
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