What question did this study set out to answer?

The research aims to develop a machine learning framework to predict the self-energy of one-dimensional Hubbard models.

April 27, 2026Open Access

Machine learning Green’s functions of strongly correlated Hubbard models

Key Points

The research aims to develop a machine learning framework to predict the self-energy of one-dimensional Hubbard models.
Utilized kernel ridge regression to encode self-energy from mean-field features.
Examined a range of on-site Coulomb interaction strengths, from weak (<U/t < 1) to strong (>U/t > 8).
Applied Dyson's equation and analytic continuation to transform predicted self-energy into real-frequency Green's functions.
Successfully predicted self-energy for both weakly and strongly correlated Hubbard models.
Enabled access to spectral functions and density of states from Green's functions.
Validated the method across nearest-neighbor and long-range hopping terms.

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-orderGWcalculations. This approach is applicable across a wide range of on-site Coulomb interaction strengthsU/t, ranging from weakly interacting systems (U/t ) 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 interactionstand long-range hopping termst',t'', andt'''.

Machine learning Green’s functions of strongly correlated Hubbard models

Key Points

Abstract

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