Extracting spectral functions from imaginary time data - the analytic continuation problem revisited
Analytic continuation is a central step in the simulation of finite-temperature field theories in which numerically obtained imaginary-time data is continued to the real frequency axis for physical interpretation. Numerical analytic continuation is an ill-posed problem in which uncertainties on the Matsubara axis are amplified exponentially. This talk introduces a new class of algorithms, based on the mathematical framework of Nevanlinna theory combined with numerical methods from signal processing and control theory, which overcome the ill-posed nature of the problem and offer systematically improvable continuations, thereby facilitating the interpretation of computational results from finite-temperature field theories.