量子蒙特卡罗模拟中斯莱特行列式更新的快速有效算法
A Fast and Efficient Algorithm for Slater Determinant Updates in Quantum Monte Carlo Simulations
摘要：
我们提出了一个有效的低秩更新算法，用于更新量子蒙特卡罗（QMC）模拟中使用的试验波函数。该算法基于Slater行列式的低秩更新。特别地，与需要O（N^2）次计算的传统算法相比，该算法在第k步期间的计算复杂度为O（kN），其中N是系统大小。对于单行列式试探波函数，新算法比传统的O（N^2）Sherman-Morrison算法快，最多可达O（N）次更新。对于M+1个行列式的多行列式组态相互作用型试探波函数，新算法的效率明显提高，节省了O（MN^2）的工作量和O（MN^2）的存储量。该算法使更准确和更有效的QMC计算使用组态相互作用型波函数。
英文摘要：
We present an efficient low-rank updating algorithm for updating the trial wavefunctions used in Quantum Monte Carlo (QMC) simulations. The algorithm is based on low-rank updating of the Slater determinants. In particular, the computational complexity of the algorithm is O(kN) during the k-th step compared with traditional algorithms that require O(N^2) computations, where N is the system size. For single determinant trial wavefunctions the new algorithm is faster than the traditional O(N^2) Sherman-Morrison algorithm for up to O(N) updates. For multideterminant configuration-interaction type trial wavefunctions of M+1 determinants, the new algorithm is significantly more efficient, saving both O(MN^2) work and O(MN^2) storage. The algorithm enables more accurate and significantly more efficient QMC calculations using configuration interaction type wavefunctions.
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