Physically interpretable approximations of many-body spectral functions

The rational function approximation provides a natural and interpretable representation of response functions such as the many-body spectral functions. We apply the Vector Fitting (VFIT) algorithm to fit a variety of spectral functions calculated from the Holstein model of electron-phonon interactions. We show that the resulting rational functions are highly efficient in their fitting of sharp features in the spectral functions, and could provide a means to infer physically relevant information from a spectral dataset. The position of the peaks in the approximated spectral function are determined by the location of poles in the complex plane. In addition, we developed an enhanced version of VFIT by introducing a regularization parameter that is slowly annealed to zero. With this new procedure, we demonstrate it is possible to achieve accurate spectral function fits that vary smoothly as a function of physical conditions.