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

Abstract

We applied machine learning methods in order to find the Green's function of the Anderson impurity model, a basic model system of quantum many-body condensed-matter physics. Furthermore, 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. Our results indicate that a machine learning approach to dynamical mean-field theory may be feasible.

Authors:
 [1];  [2];  [3];  [1]
  1. Columbia Univ., New York, NY (United States). Dept. of Physics
  2. Argonne National Lab. (ANL), Argonne, IL (United States). Materials Science Division
  3. Univ. of Basel (Switzerland). Inst. of Physics Chemistry; Argonne National Lab. (ANL), Argonne, IL (United States). Argonne Leadership Computing Facility
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC); National Science Foundation (NSF)
OSTI Identifier:
1357598
Alternate Identifier(s):
OSTI ID: 1180270
Grant/Contract Number:  
AC02-06CH11357; 3F-3138
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review. B, Condensed Matter and Materials Physics
Additional Journal Information:
Journal Volume: 90; Journal Issue: 15; Journal ID: ISSN 1098-0121
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 97 MATHEMATICS AND COMPUTING

Citation Formats

Arsenault, Louis-François, Lopez-Bezanilla, Alejandro, von Lilienfeld, O. Anatole, and Millis, Andrew J. Machine learning for many-body physics: The case of the Anderson impurity model. United States: N. p., 2014. Web. doi:10.1103/PhysRevB.90.155136.
Arsenault, Louis-François, Lopez-Bezanilla, Alejandro, von Lilienfeld, O. Anatole, & Millis, Andrew J. Machine learning for many-body physics: The case of the Anderson impurity model. United States. doi:10.1103/PhysRevB.90.155136.
Arsenault, Louis-François, Lopez-Bezanilla, Alejandro, von Lilienfeld, O. Anatole, and Millis, Andrew J. Fri . "Machine learning for many-body physics: The case of the Anderson impurity model". United States. doi:10.1103/PhysRevB.90.155136. https://www.osti.gov/servlets/purl/1357598.
@article{osti_1357598,
title = {Machine learning for many-body physics: The case of the Anderson impurity model},
author = {Arsenault, Louis-François and Lopez-Bezanilla, Alejandro and von Lilienfeld, O. Anatole and Millis, Andrew J.},
abstractNote = {We applied machine learning methods in order to find the Green's function of the Anderson impurity model, a basic model system of quantum many-body condensed-matter physics. Furthermore, 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. Our results indicate that a machine learning approach to dynamical mean-field theory may be feasible.},
doi = {10.1103/PhysRevB.90.155136},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 15,
volume = 90,
place = {United States},
year = {2014},
month = {10}
}

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Cited by: 25 works
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