Machine learning for many-body physics: The case of the Anderson impurity model
This work addresses a computational bottleneck in condensed-matter physics for researchers studying quantum many-body systems, but it is incremental as it builds on existing methods with a new parametrization.
The authors tackled the problem of finding the Green's function for the Anderson impurity model, a key quantum many-body system, by applying machine learning methods and found that a Legendre polynomial representation reduced errors with limited coefficients, making a machine learning approach to dynamical mean-field theory potentially feasible.
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.