Nevanlinna Analytical Continuation

Simulations of finite temperature quantum systems provide imaginary frequency Green's functions that correspond one-to-one to experimentally measurable real-frequency spectral functions. However, due the bad conditioning continuation transform from real frequencies, established methods tend either wash out features at high frequencies or produce with unphysical negative parts. Here, we show explicitly respecting analytic `Nevanlinna' structure function leads intrinsically positive and normalized functions, present a continued fraction expansion yields all possible consistent structure. Application synthetic trial data shows sharp, smooth, multi-peak is resolved accurately. band silicon demonstrates energy are precisely. Continuations in realistic correlated setup reveal additional were previously unresolved. By substantially increasing resolution calculations our work overcomes one main limitations finite-temperature simulations.