skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Journal Article · · Physical Review. B, Condensed Matter and Materials Physics
 [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
+ Show Author Affiliations

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.

Research Organization:
Argonne National Laboratory (ANL), Argonne, IL (United States)
Sponsoring Organization:
USDOE Office of Science (SC); National Science Foundation (NSF)
Grant/Contract Number:
AC02-06CH11357; 3F-3138
OSTI ID:
1357598
Alternate ID(s):
OSTI ID: 1180270
Journal Information:
Physical Review. B, Condensed Matter and Materials Physics, Vol. 90, Issue 15; ISSN 1098-0121
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 104 works
Citation information provided by
Web of Science

References (46)

Computational Complexity and Fundamental Limitations to Fermionic Quantum Monte Carlo Simulations journal May 2005
Finding Density Functionals with Machine Learning journal June 2012
Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning journal January 2012
Machine learning of molecular electronic properties in chemical compound space journal September 2013
Modeling electronic quantum transport with machine learning journal June 2014
Potential energy surfaces for macromolecules. A neural network technique journal May 1992
Representing high-dimensional potential-energy surfaces for reactions at surfaces by neural networks journal September 2004
A random-sampling high dimensional model representation neural network for building potential energy surfaces journal August 2006
Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces journal April 2007
Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons journal April 2010
Correlated Lattice Fermions in d = ∞ Dimensions journal January 1989
Hubbard model in infinite dimensions journal March 1992
Hubbard model in infinite dimensions: A quantum Monte Carlo study journal July 1992
Continuous-Time Solver for Quantum Impurity Models journal August 2006
Quantum Monte Carlo impurity solver for cluster dynamical mean-field theory and electronic structure calculations with adjustable cluster base journal April 2007
Continuous-time Monte Carlo methods for quantum impurity models journal May 2011
Assessment and Validation of Machine Learning Methods for Predicting Molecular Atomization Energies journal July 2013
The Elements of Statistical Learning book January 2009
Towards an exact solution of the Anderson model journal November 1980
Analytical approximation for single-impurity Anderson model journal March 2010
Dynamical properties of the Anderson impurity model within a diagrammatic pseudoparticle approach journal October 2004
Monte Carlo Method for Magnetic Impurities in Metals journal June 1986
Electronic correlation in nanoscale junctions: Comparison of the GW approximation to a numerically exact solution of the single-impurity Anderson model journal January 2008
Numerical renormalization group method for quantum impurity systems journal April 2008
Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions journal January 1996
Correlated electrons in high-temperature superconductors journal July 1994
Theory of the atomic limit of the Anderson model. I. Perturbation expansions re-examined journal December 1978
Benchmark of a modified iterated perturbation theory approach on the fcc lattice at strong coupling journal August 2012
Orthogonal polynomial representation of imaginary-time Green’s functions journal August 2011
A Fast, Simple, and Stable Chebyshev--Legendre Transform Using an Asymptotic Formula journal January 2014
Exact diagonalization approach to correlated fermions in infinite dimensions: Mott transition and superconductivity journal March 1994
Block Lanczos tridiagonalization of complex symmetric matrices conference August 2005
Correlated Lattice Fermions in d = ∞ Dimensions journal February 1989
Optimization of probiotic therapeutics using machine learning in an artificial human gastrointestinal tract journal January 2021
Modeling electronic quantum transport with machine learning text January 2014
Machine learning of molecular electronic properties in chemical compound space text January 2013
Towards an Exact Solution of the Anderson Model book August 1996
Fast and accurate modeling of molecular atomization energies with machine learning text January 2012
The Elements of Statistical Learning book January 2001
Gaussian Approximation Potentials: the accuracy of quantum mechanics, without the electrons text January 2009
Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning text January 2011
Modeling Electronic Quantum Transport with Machine Learning text January 2014
A continuous-time solver for quantum impurity models text January 2005
The numerical renormalization group method for quantum impurity systems text January 2007
Correlated Electrons in High Temperature Superconductors text January 1993
Machine learning of molecular electronic properties in chemical compound space text January 2013

Cited By (39)

Machine Learning, Quantum Chemistry, and Chemical Space book January 2017
Quantum Machine Learning in Chemical Compound Space journal March 2018
Feature vector clustering molecular pairs in computer simulations journal July 2019
Crystal structure representations for machine learning models of formation energies journal April 2015
Machine learning phases of matter journal February 2017
Quantum machine learning for electronic structure calculations journal October 2018
Pattern Learning Electronic Density of States journal April 2019
Electronic spectra from TDDFT and machine learning in chemical space journal August 2015
Projected regression method for solving Fredholm integral equations arising in the analytic continuation problem of quantum physics journal October 2017
Machine learning & artificial intelligence in the quantum domain: a review of recent progress journal June 2018
From DFT to machine learning: recent approaches to materials science–a review journal May 2019
Deep learning and the Schrödinger equation journal October 2017
Accelerated continuous time quantum Monte Carlo method with machine learning journal July 2019
Analytic continuation via domain knowledge free machine learning journal December 2018
Self-organizing maps as a method for detecting phase transitions and phase identification journal January 2019
Matrix product operators for sequence-to-sequence learning journal October 2018
Discriminative Cooperative Networks for Detecting Phase Transitions journal April 2018
Mapping and classifying molecules from a high-throughput structural database journal February 2017
Quantum error correction for the toric code using deep reinforcement learning journal September 2019
Electronic spectra from TDDFT and machine learning in chemical space text January 2015
Crystal structure representations for machine learning models of formation energies text January 2015
Electronic Spectra from TDDFT and Machine Learning in Chemical Space text January 2015
Comparing molecules and solids across structural and alchemical space text January 2016
Machine learning phases of matter text January 2016
Discovering Phase Transitions with Unsupervised Learning text January 2016
Machine Learning Phases of Strongly Correlated Fermions text January 2016
Mapping and Classifying Molecules from a High-Throughput Structural Database preprint January 2016
Identifying polymer states by machine learning text January 2017
Extensive deep neural networks for transferring small scale learning to large scale systems text January 2017
Machine Learning Topological Invariants with Neural Networks text January 2017
Neural-Network Quantum States, String-Bond States, and Chiral Topological States text January 2017
Self-learning Monte Carlo with Deep Neural Networks text January 2018
Matrix Product Operators for Sequence to Sequence Learning text January 2018
Machine learning of phase transitions in the percolation and XY models text January 2018
Probing hidden spin order with interpretable machine learning text January 2018
Deep Learning Topological Invariants of Band Insulators text January 2018
Pattern Learning Electronic Density of States text January 2018
Self-organizing maps as a method for detecting phase transitions and phase identification text January 2018
Machine learning density functional theory for the Hubbard model text January 2018

Similar Records

Machine learning of Kondo physics using variational autoencoders and symbolic regression
Journal Article · Mon Dec 06 00:00:00 EST 2021 · Physical Review. B · OSTI ID:1357598
+4 more
Predicting impurity spectral functions using machine learning
Journal Article · Mon Jun 14 00:00:00 EDT 2021 · Physical Review. B · OSTI ID:1357598
+2 more
Optimizing Kernel Machines Using Deep Learning
Journal Article · Tue Mar 06 00:00:00 EST 2018 · IEEE Transactions on Neural Networks and Learning Systems · OSTI ID:1357598
+1 more

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
97 MATHEMATICS AND COMPUTING