A simple approach towards the sign problem using path optimisation
A simple approach towards the sign problem using path optimisation
复制标题
使用路径优化解决符号问题的简单方法
DOI：
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发表时间：
2018
影响因子：
5.4
通讯作者：
M. Kroyter
中科院分区：
文献类型：
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作者：
F. Bursa;M. Kroyter
BSTRACTWE提出了一种用符号问题模拟理论的方法，该方法依赖于不限于Lefschetz Thimbles的复杂整合轮廓在这种情况下，确定对符号问题的主要贡献，是来自最近的邻居交互，并大约通过集成轮廓的明确变形来取消它根据一组参数，我们在较小的晶格上找到了这些参数的最佳值，并研究了它们的有效性范围提出了评估与轮廓变形相关的雅各布式的方法，并检查了其数值稳定性。从L≈32到L≈700变得严重。对Jacobian（O（l）扫描）的有效评估导致在标准笔记本电脑上的运行时间为几分钟。
A bstractWe suggest an approach for simulating theories with a sign problem that relies on optimisation of complex integration contours that are not restricted to lie along Lefschetz thimbles. To that end we consider the toy model of a one-dimensional Bose gas with chemical potential. We identify the main contribution to the sign problem in this case as coming from a nearest neighbour interaction and approximately cancel it by an explicit deformation of the integration contour. We extend the obtained expressions to more general ones, depending on a small set of parameters. We find the optimal values of these parameters on a small lattice and study their range of validity. We also identify precursors for the onset of the sign problem. A fast method of evaluating the Jacobian related to the contour deformation is proposed and its numerical stability is examined. For a particular choice of lattice parameters, we find that our approach increases the lattice size at which the sign problem becomes serious from L ≈ 32 to L ≈ 700. The efficient evaluation of the Jacobian (O(L) for a sweep) results in running times that are of the order of a few minutes on a standard laptop.
DOI：
10.1088/1742-6596/706/2/022004
发表时间：
2015-12
期刊：
Journal of Physics: Conference Series
影响因子：
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作者：
G. Aarts
通讯作者：
G. Aarts
随机量化可以避免符号问题吗？
影响因子：
8.6
作者：
Aarts G
通讯作者：
Aarts G
影响因子：
5
作者：
G. Aarts;E. Seiler;I. Stamatescu
通讯作者：
G. Aarts;E. Seiler;I. Stamatescu