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

Louis-François Arsenault, Alejandro Lopez-Bezanilla, O. Anatole von Lilienfeld, and Andrew J. Millis

Phys. Rev. B 90, 155136 – Published 31 October 2014

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.

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Received 6 August 2014
Revised 22 September 2014

DOI:https://doi.org/10.1103/PhysRevB.90.155136

Authors & Affiliations

Louis-François Arsenault^1,*, Alejandro Lopez-Bezanilla², O. Anatole von Lilienfeld^3,4, and Andrew J. Millis¹

¹Department of Physics, Columbia University, New York, New York 10027, USA
²Materials Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Lemont, Illinois 60439, USA
³Institute of Physical Chemistry, Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
⁴Argonne Leadership Computing Facility, Argonne National Laboratory, 9700 South Cass Avenue, Lemont, Illinois 60439, USA

^*la2518@columbia.edu

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Vol. 90, Iss. 15 — 15 October 2014

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