Automated label flows for excited states of correlation functions in lattice gauge theory

Extracting excited states from lattice gauge theory correlation functions can be achieved through χ^{2} minimization fits or algebraic approaches such as the variational method and Prony's method. Performing any kind of error analysis often leads to overlapping confidence regions of model parameters, even when the spectrum is not particularly dense. To correctly estimate errors, one must beware of mislabeling the states. In this work, we provide an algorithm that we call automated label flows which consistently and systematically identifies a deterministic labeling of states. This is a black-box approach in the sense that it gives a sensible set of labels without user guidance. As an example, we pair one black box method with another, analyzing a lattice correlation function from real data using automated label flows in the context of Prony's method.