Minimal Neural Network to Learn the Metal-insulator Transition in the Dynamical Mean-field Theory

Abstract

We present a minimal neural network model to learn classifying the metallic and insulating phases from the real-frequency hybridization function computed in the dynamical mean-field theory for the repulsive Hubbard model at half-filling. The resulting neural network discriminates the phases essentially by reading the presence of the quasiparticle peak. The pattern observed in the weight matrix of neural connectivity allows us to write down a simple form of an indicator that can precisely detect the transition point only with the bath parameters building the Anderson impurity model. The proposed transition indicator is very sensitive to the emergence of zero energy orbital in the quantum bath. We demonstrate the accuracy of the indicator in the discrete bath description with a few orbitals for the exact diagonalization solver.