Machine learning for many-body physics: The case of the Anderson impurity model

TL;DR

This paper explores machine learning techniques to efficiently compute the Green's function of the Anderson impurity model, demonstrating the potential for ML to enhance dynamical mean-field theory in quantum many-body physics.

Contribution

It introduces a Legendre polynomial parametrization for Green's functions, showing improved accuracy and efficiency over other methods in the context of many-body physics.

Findings

Legendre polynomial representation reduces the number of coefficients needed.

Machine learning errors decrease with larger training sets.

ML approach shows promise for dynamical mean-field theory applications.

Abstract

Machine learning methods are applied to finding the Green's function of the Anderson impurity model, a basic model system of quantum many-body condensed-matter physics. Different methods of parametrizing the Green's function are investigated; a representation in terms of Legendre polynomials is found to be superior due to its limited number of coefficients and its applicability to state of the art methods of solution. The dependence of the errors on the size of the training set is determined. The results indicate that a machine learning approach to dynamical mean-field theory may be feasible.