标题： 高阶复杂积分路径的优化 显示英文标题

标题： Optimisation of complex integration contours at higher order

摘要： 我们继续研究轮廓变形作为一种处理符号问题的实际工具，以具有非零化学势的$d$维玻色子气体作为玩具模型。 我们推导出关于自然小参数直到二阶的轮廓的显式表达式，并将这些轮廓推广为一个假设，使得雅可比量的计算快速（$O(1)$）。 我们考察了各种提出的轮廓作为时空维度、化学势和格点大小与几何形状函数的行为，并用平均相位因子作为符号问题严重程度的度量。 结果表明，这种方法显著减少了符号问题，并且随着时空维度的增加，它变得更加高效。 对$\operatorname{Im}\langle S \rangle$的贡献之间的相关性在确定平均相位因子方面起着关键作用，我们详细检查了这些相关性。 显示英文摘要

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.