Finite-size errors in continuum quantum Monte Carlo calculations
Finite-size errors in continuum quantum Monte Carlo calculations
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DOI：
10.1103/physrevb.78.125106
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发表时间：
2008-09-01
影响因子：
3.7
通讯作者：
Foulkes, W. M. C.
中科院分区：
文献类型：
--
作者：
Drummond, N. D.;Needs, R. J.;Foulkes, W. M. C.
分析了量子蒙特卡罗（QMC）能量数据中有限尺寸误差的消除问题。我们证明，（i）添加最近提出的[S。Chiesa等人，物理修订信函97，076404（2006）]有限尺寸校正的埃瓦尔德能量和（ii）使用模型周期库仑（MPC）相互作用[L. M. Fraser等人，物理学评论B 53，1814（1996）; C.肯特等人，Phys. Rev. B 59，1917（1999）; A. J.威廉姆森等人，Phys. Rev. B 55，R4851（1997）]是从立方系统中的相互作用能中去除有限尺寸效应的问题的良好解决方案，前提是交换相关（XC）空穴已经相对于系统尺寸收敛。然而，我们发现，MPC相互作用扭曲的XC孔在有限系统中，这意味着埃瓦尔德相互作用应该被用来产生的配置分布。Chiesa等人[Phys. Rev. Lett. 97，076404（2006）]在低对称性系统中是不完整的。超越领先的顺序修正的动能被认为是必要的，在中等和高密度，我们调查的效果添加这样的修正QMC数据的均匀电子气。我们分析了二维系统中的有限大小的错误，并表明，领先的顺序行为不同于迄今为止一直假设的。我们比较了不同的扭曲平均方法减少单粒子有限尺寸误差的效率，我们研究了各种有限尺寸外推公式的性能。最后，我们研究了扩散QMC中偏差的系统尺度标度。
We analyze the problem of eliminating finite-size errors from quantum Monte Carlo (QMC) energy data. We demonstrate that both (i) adding a recently proposed [S. Chiesa et al., Phys. Rev. Lett. 97, 076404 (2006)] finite-size correction to the Ewald energy and (ii) using the model periodic Coulomb (MPC) interaction [L. M. Fraser et al., Phys. Rev. B 53, 1814 (1996); P. R. C. Kent et al., Phys. Rev. B 59, 1917 (1999); A. J. Williamson et al., Phys. Rev. B 55, R4851 (1997)] are good solutions to the problem of removing finite-size effects from the interaction energy in cubic systems provided the exchange-correlation (XC) hole has converged with respect to system size. However, we find that the MPC interaction distorts the XC hole in finite systems, implying that the Ewald interaction should be used to generate the configuration distribution. The finite-size correction of Chiesa et al. [Phys. Rev. Lett. 97, 076404 (2006)] is shown to be incomplete in systems of low symmetry. Beyond-leading-order corrections to the kinetic energy are found to be necessary at intermediate and high densities; we investigate the effect of adding such corrections to QMC data for the homogeneous electron gas. We analyze finite-size errors in two-dimensional systems and show that the leading-order behavior differs from that which has hitherto been supposed. We compare the efficiencies of different twist-averaging methods for reducing single-particle finite-size errors and we examine the performance of various finite-size extrapolation formulas. Finally, we investigate the system-size scaling of biases in diffusion QMC.