Mishchenko Yuriy
Cold Spring Harbor Laboratory, Cold Spring Harbor, New York 11743, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Feb;73(2 Pt 2):026706. doi: 10.1103/PhysRevE.73.026706. Epub 2006 Feb 22.
We suggest an exact approach to help remedy the fermion sign problem in diffusion quantum Monte Carlo simulations. The approach is based on an explicit suppression of symmetric modes in the Schrödinger equation by means of a modified stochastic diffusion process (antisymmetric diffusion process). We introduce this algorithm and illustrate it on potential models in one dimension (1D) and show that there it solves the fermion sign problem exactly and converges to the lowest antisymmetric state of the system. Then, we discuss extensions of this approach to many-dimensional systems on examples of quantum oscillator in 2D-20D and a toy model of three and four fermions on harmonic strings in 2D and 3D. We show that in all these cases our method shows a performance comparable to that of a fixed-node approximation with an exact node.
我们提出一种精确方法，以帮助解决扩散量子蒙特卡罗模拟中的费米子符号问题。该方法基于通过修改后的随机扩散过程（反对称扩散过程）对薛定谔方程中的对称模式进行显式抑制。我们介绍此算法，并在一维（1D）势模型上进行说明，结果表明该算法能精确解决费米子符号问题，并收敛到系统的最低反对称态。然后，我们以二维至二十维的量子振子以及二维和三维中谐波弦上的三个和四个费米子的玩具模型为例，讨论该方法在多维系统中的扩展。我们表明，在所有这些情况下，我们的方法表现出与具有精确节点的固定节点近似相当的性能。
