Machine Learned Spectral Functions for the Quantum Impurity Problem

Machine learning techniques can greatly reduce simulation times by providing highly accurate approximations, thus circumventing the need for more expensive models. This work leverages a feed-forward neural network (NN) to predict the spectral functions of the single impurity Anderson model (SIAM) as a function of five physical parameters including the Coulomb interaction U, hybridization constant Γ, impurity energy ε_d, magnetic field B, and temperature T. The NN was trained on ~670,000 unique SIAM system spectral functions generated by Wilson’s Numerical Renormalization Group (NRG). The NN predicts the spectral function with a mean absolute difference of less than 3% compared to the ground truth. The ability to efficiently predict a spectral function for the quantum impurity problem can improve the computation time for dynamical mean field theory and related methods that investigate strong correlation in condensed matter systems.

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