论文标题
复杂耦合处的晶格标量场理论
Lattice Scalar Field Theory At Complex Coupling
论文作者
论文摘要
当耦合常数复杂时，晶格标量场理论会遇到一个符号问题。这是遭受晶格Schwinger-keldysh形式主义的实时标志问题的近亲，也是Fermion符号问题的更遥远的亲戚，它困扰着有限密度的QCD计算。我们演示了分别以$ 0+1 $和$ 1+1 $尺寸的标量字段上复杂的归一化流和轮廓变形的方法。在这两种情况下，棘手的符号问题都很容易绕过。这些方法扩展到负耦合，其中只能通过分析延续来定义分区函数。最后，我们检查了分区函数零的位置，并讨论了它们与这些算法的性能的关系。
Lattice scalar field theories encounter a sign problem when the coupling constant is complex. This is a close cousin of the real-time sign problems that afflict the lattice Schwinger-Keldysh formalism, and a more distant relative of the fermion sign problem that plagues calculations of QCD at finite density. We demonstrate the methods of complex normalizing flows and contour deformations on scalar fields in $0+1$ and $1+1$ dimensions, respectively. In both cases, intractable sign problems are readily bypassed. These methods extend to negative couplings, where the partition function can be defined only by analytic continuation. Finally, we examine the location of partition function zeros, and discuss their relation to the performance of these algorithms.
