Improving Spectral Resolution from Real-Time Evolution for Correlated Systems

The quality of numerically simulated spectra using real-time evolution methods for strongly correlated systems is affected by the length of simulation time and the system size, limiting both frequency and momentum resolution. Here, we propose a computationally cheap, linear autoregressive machine learning-based framework to learn directly from spectral functions, or more precisely correlation functions χ(r,t), bypassing the need to represent the many-body wavefunction itself. We demonstrate the method by extending the lesser Green's function for both the Hubbard model and more computationally challenging Hubbard-extended Holstein model, significantly improving both the frequency and momentum resolution of the single-particle removal spectrum A(k,ω) and allowing observation of otherwise obscured spectral features due to electron-phonon coupling.