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

Automated summary

By explicitly respecting the analytic Nevanlinna structure of Green's function, this study shows that positive and normalized spectral functions can be obtained, and presents a continued fraction expansion method to derive all possible functions consistent with the analytic structure. Application to synthetic trial data and the band structure of silicon demonstrate the accurate resolution of sharp, smooth, and multipeak data, as well as high energy features. Continuations in a realistic correlated setup reveal previously unresolved additional features, substantially increasing the resolution of real frequency calculations and overcoming a main limitation of finite-temperature quantum simulations.