Correlations and Coherence at Different Scales (CCDS25)

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 considered to be an ill-posed problem where uncertainties on the Matsubara axis are amplified exponentially. This talk introduces 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.