Machine learning Green’s functions of strongly correlated Hubbard models

We demonstrate that a machine learning framework based on kernel ridge regression can encode and predict the self-energy of one-dimensional Hubbard models using only mean-field features such as static and dynamic Hartree–Fock quantities and first-order GW calculations. This approach is applicable across a wide range of on-site Coulomb interaction strengths U/t, ranging from weakly interacting systems ( U/t≪1) to strong correlations ( U/t>8). The predicted self-energy is transformed via Dyson’s equation and analytic continuation to obtain the real-frequency Green’s function, which allows access to the spectral function and density of states. This method can be used for nearest-neighbor interactions t and long-range hopping terms t′, t′′, and t′′′.