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Emerging sampling algorithms based on normalizing flows have the potential tosolve ergodicity problems in lattice calculations. Furthermore, it has beennoted that flows can be used to compute thermodynamic quantities which aredifficult to access with traditional methods. This suggests that they are alsoapplicable to the density-of-states approach to complex action problems. Inparticular, flow-based sampling may be used to compute the density directly, incontradistinction to the conventional strategy of reconstructing it viameasuring and integrating the derivative of its logarithm. By circumventingthis procedure, the accumulation of errors from the numerical integration isavoided completely and the overall normalization factor can be determinedexplicitly. In this proof-of-principle study, we demonstrate our method in thecontext of two-component scalar field theory where the $O(2)$ symmetry isexplicitly broken by an imaginary external field. First, we concentrate on thezero-dimensional case which can be solved exactly. We show that with ourmethod, the Lee-Yang zeroes of the associated partition function can besuccessfully located. Subsequently, we confirm that the flow-based approachcorrectly reproduces the density computed with conventional methods in one- andtwo-dimensional models.

Flow-based density of states for complex actions