Das Dyutiman, Martin Richard M, Kalos Malvin H
University of Illinois at Urbana-Champaign, 1110 W. Green Street, Urbana, Illinois 61801, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Apr;73(4 Pt 2):046702. doi: 10.1103/PhysRevE.73.046702. Epub 2006 Apr 18.
The quantum Monte Carlo (QMC) technique is an extremely powerful method to treat many-body systems. Usually the quantum Monte Carlo method has been applied in cases where the interaction potential has a simple analytic form, like the 1/r Coulomb potential. However, in a complicated environment as in a semiconductor heterostructure, the evaluation of the interaction itself becomes a nontrivial problem. Obtaining the potential from any grid-based finite-difference method for every walker and every step is infeasible. We demonstrate an alternative approach of solving the Poisson equation by a classical Monte Carlo calculation within the overall quantum Monte Carlo scheme. We have developed a modified "walk on spheres" algorithm using Green's function techniques, which can efficiently account for the interaction energy of walker configurations, typical of quantum Monte Carlo algorithms. This stochastically obtained potential can be easily incorporated with variational, diffusion, and other Monte Carlo techniques. We demonstrate the validity of this method by studying a simple problem, the polarization of a helium atom in the electric field of an infinite capacitor.
量子蒙特卡罗（QMC）技术是处理多体系统的一种极其强大的方法。通常，量子蒙特卡罗方法已应用于相互作用势具有简单解析形式的情况，如1/r库仑势。然而，在半导体异质结构这样复杂的环境中，相互作用本身的评估成为一个棘手的问题。对于每个游走粒子和每一步，从任何基于网格的有限差分方法获得势是不可行的。我们展示了一种在整体量子蒙特卡罗方案中通过经典蒙特卡罗计算求解泊松方程的替代方法。我们利用格林函数技术开发了一种改进的“球上行走”算法，它可以有效地考虑游走粒子构型的相互作用能，这是量子蒙特卡罗算法的典型特征。这种通过随机获得的势可以很容易地与变分、扩散和其他蒙特卡罗技术相结合。我们通过研究一个简单问题，即无限电容器电场中氦原子的极化，来证明该方法的有效性。
