论文标题
费米符号问题的通用解决方案
A Generic Solution of Fermion Sign Problem
论文作者
论文摘要
本文完全解决了量子蒙特卡洛计算的最大障碍，这是费米的标志问题。在这里，我们找到了一种策略，其中这些负加权路径的贡献被彻底取消或被一些积极加权的路径所取代。关键点位于我们组中提出的Feynman路径积分公式上，这使我们能够深入分析每条路径的玻璃体重量。通过数学证明，我们证明了物理量可以在特定类型的路径中精确计算，这些路径具有阳性的玻尔兹曼重量。有了这一发现，提出了一种新的蒙特卡洛方法，其中不存在fermion符号问题。例如，当前方法应用于二维Hubbard模型，结果确实表明了正确性。
The fermion sign problem, the biggest obstacle in quantum Monte Carlo calculations, is completely solved in this paper. Here, we find a strategy, in which the contribution from those negative-weighted paths is thoroughly cancelled or replaced by some positive-weighted paths. The crucial point lies on the Feynman path integral formula proposed in our group, which allows us to deeply analyze the Boltzmann weight of each path. Through mathematical proof, we demonstrate that physical quantities can be exactly calculated within a specific kind of paths, which have positive the Boltzmann weight. With this finding, a new Monte Carlo method is proposed, in which the fermion sign problem is absent. As an example, the current method is applied to the two-dimensional Hubbard model, and the results do manifest the correctness.
