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 chi-squared minimization fits or algebraic approaches such as the variational method and Prony's method. Performing any kind of error analysis, such as bootstrap resampling, often leads to overlapping confidence regions of model parameters, even when the spectrum is not particularly dense. In order 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. In the context of Prony's method, we analyze lattice correlation functions by using automated label flows, and compare the results to fits obtained from chi-square minimization fits to exponentials.