高阶复杂积分等值线的优化
Optimisation of complex integration contours at higher order
摘要：
我们继续我们的研究轮廓变形作为一个实用的工具，用于处理的符号问题，使用$d$维玻色气体与非零化学势作为玩具模型。我们推导出显式表达式的轮廓高达二阶相对于一个自然的小参数，并概括这些轮廓的一个anasterian的雅可比矩阵的评价是快速的（$O(1)$）。我们研究的行为的各种拟议的轮廓作为一个功能的时空维度，化学势，晶格的大小和几何形状，并使用平均相位因子作为衡量的严重性的标志问题。事实证明，这种方法导致了一个显着减少的符号问题，它变得更有效的空间-时间维度的增加。贡献之间的相关性$\operatorname{Im}\langle S \rangle$起着关键作用，在确定平均相位因子，我们详细研究这些相关性。
英文摘要：
We continue our study of contour deformation as a practical tool for dealing with the sign problem using the $d$-dimensional Bose gas with non-zero chemical potential as a toy model. We derive explicit expressions for contours up to the second order with respect to a natural small parameter and generalise these contours to an ansatz for which the evaluation of the Jacobian is fast ($O(1)$). We examine the behaviour of the various proposed contours as a function of space-time dimensionality, the chemical potential, and lattice size and geometry and use the mean phase factor as a measure of the severity of the sign problem. In turns out that this method leads to a substantial reduction of the sign problem and that it becomes more efficient as space-time dimensionality is increased. Correlations among contributions to $\operatorname{Im}\langle S \rangle$ play a key role in determining the mean phase factor and we examine these correlations in detail.
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