Complex Pole Representation in Frequency and Its Applications to Many-Body Problems

Accurately representing correlation functions of continuous systems using a small set of discrete degrees of freedom is a central challenge in quantum many-body simulations. In this talk, we introduce a method that achieves a compact frequency-domain representation based on a set of complex poles located in the lower-half plane. By minimizing the number of poles, we demonstrate [1] that the spectral function recovered from the ill-posed numerical analytic continuation of Matsubara data becomes systematically improvable. Extensive benchmarks on realistic systems [2] confirm the method's accuracy and robustness. We further discuss its applications to compact representations of correlation functions [3] and bath fitting [4], and present an open-source software package, MiniPole.