Machine Learning Green's Functions of Strongly Correlated Hubbard Models

Abstract

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 ($U/t\ll 1$) 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 $t^{\prime }$, $t^{\prime \prime }$, and $t^{\prime \prime \prime }$.

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