Accelerated calculation of impurity Green's functions exploiting the extreme Mpemba effect

Simulating the dynamics of quantum impurity models remains a fundamental challenge due to the complex memory effects that arise from system-environment interactions. Of particular interest are two-time correlation functions of an impurity, which are central to the characterization of these many-body systems, and are a cornerstone of the description of correlated materials in dynamical mean field theory (DMFT). In this work, we extend our previous work on the extrapolation of single-time observables to demonstrate an efficient scheme for computing two-time impurity correlation functions, by combining the non-Markovian quantum Mpemba effect (NMQMpE) with a dynamical map-based framework for open quantum systems. Our method is benchmarked against exact and known accurate results in prototypical impurity models for both fermionic and bosonic environments, demonstrating significant computational savings compared to state-of-the-art methods.