Physics-Informed featurization of spectral functions

Spectral functions are key observables of interacting many-body systems, and characterizing them is of great interest. We investigate two methods for approximating spectral functions via rational approximations, i.e., approximations as a ratio of two polynomials. The first approach, VFIT, approximates individual spectral functions of lattice polaron models in a reliable, simple, and accurate way. We also introduce a second fitting procedure, which we call the Smooth Rational Approximation (SRA), that simultaneously fits an entire batch of spectral functions. This fitting procedure can be regularized such that the predicted spectral functions vary smoothly with the governing physical parameters.