Emerging sampling algorithms based on normalizing flows have the potential to solve ergodicity problems in lattice calculations. Furthermore, it has been noted that flows can be used to compute thermodynamic quantities which are difficult to access with traditional methods. This suggests that they are also applicable to the density-of-states approach to complex action problems. In particular, flow-based sampling may be used to compute the density directly, in contradistinction to the conventional strategy of reconstructing it via measuring and integrating the derivative of its logarithm. By circumventing this procedure, the accumulation of errors from the numerical integration is avoided completely and the overall normalization factor can be determined explicitly. In this proof-of-principle study, we demonstrate our method in the context of two-component scalar field theory where the $O(2)$ symmetry is explicitly broken by an imaginary external field. First, we concentrate on the zero-dimensional case which can be solved exactly. We show that with our method, the Lee-Yang zeroes of the associated partition function can be successfully located. Subsequently, we confirm that the flow-based approach correctly reproduces the density computed with conventional methods in one- and two-dimensional models.

翻译：基于正则化流的涌现采样算法有潜力解决格点计算中的遍历性问题。此外，已有研究指出，流可用于计算传统方法难以获取的热力学量。这表明流同样适用于复作用量问题中的态密度方法。与通过测量并对数导数积分来重建态密度的传统策略不同，基于流的采样可直接计算态密度。通过规避这一过程，数值积分产生的误差累积被完全消除，且整体归一化因子可被显式确定。在本原理验证研究中，我们以两分量标量场理论为背景，展示了该方法——其中$O(2)$对称性被虚外场显式破缺。首先聚焦于可精确求解的零维情形，证明该方法能成功定位关联配分函数的李-杨零点。随后，我们验证了基于流的方法在一维和二维模型中正确复现了用传统方法计算的态密度。