Deep learning route to quantum materials: A domain agnostic analytic continuation mapping

In recent years, numerous techniques have been developed to improve our understanding of the physical principles governing quantum materials. Such systems exhibit highly unusual behavior in response to variations in chemical composition, temperature, and pressure. For instance, some are insulators in some regions of the phase diagram, or poorly conducting metals, but nonetheless become high-temperature superconductors at optimal doping, as temperature decreases. Electron–electron interactions, along with disorder and inhomogeneity, have been identified as crucial factors in this class of materials. Disorder plays a significant role in tuning the critical temperature Tc, making these materials promising candidates for novel technological applications. Furthermore, recent advancements in machine learning, coupled with the extended availability of theoretically and experimentally generated datasets, create an ideal environment for accelerating quantum materials research, facilitating deeper understanding and even potential discovery of entirely new materials. In this work, we focus on a specific calculation of the density of states within the context of metal–insulator transitions. We employ the statistical Dynamical Mean Field Theory (statDMFT) and Quantum Monte Carlo (QMC) methods to solve the local impurity problem in the Matsubara frequency domain, generating a large number of Green’s functions in the Matsubara frequency domain and their corresponding spectral functions. We use these duals to train a deep neural network architecture that acts as a mapping from the discretized Matsubara frequency domain to the discretized real frequency domain, enabling physical interpretation.