Minimal pole representation and analytic continuation of matrix-valued correlation functions

The authors present here a method for analytically continuing matrix-valued correlation functions to the real axis, accurately capturing off-diagonal elements to enhance the interpretation of self-energies and susceptibilities. Based on a minimal information criterion, a selection of poles in the complex plane results in a universal noise-resistant approximation that converges reliably with increasing data precision. Comparisons with state-of-the-art techniques highlight its resolution and efficiency, establishing it as a significant advancement in computational quantum physics.