Machine learning opens new avenues for modeling correlated materials. Quantum embedding approaches, such as dynamical mean-field theory (DMFT), provide corrections to first-principles calculations for strongly correlated materials, which are poorly described at lower levels of theory. Such embedding approaches are computationally demanding on classical computing architectures, and hence remain restricted to small systems, which limits the scope of applicability without exceptional computational resources. Here we outline a data-driven machine-learning process for solving the Anderson impurity model (AIM)---the central component of DMFT calculations. The key advance is the use of an ensemble error-correction approach to generate fast and accurate solutions of AIM. An example calculation of the Mott transition using DMFT in the single band Hubbard model is given as an example of the technique, and is validated against the most accurate available method. This approach is called data-driven dynamical mean-field theory ( ${\mathbf{d}}^{3}\mathbf{MFT}$ ).Machine learning opens new avenues for modeling correlated materials. Quantum embedding approaches, such as dynamical mean-field theory (DMFT), provide corrections to first-principles calculations for strongly correlated materials, which are poorly described at lower levels of theory. Such embedding approaches are computationally demanding on classical computing architectures, and hence remain restricted to small systems, which limits the scope of applicability without exceptional computational resources. Here we outline a data-driven machine-learning process for solving the Anderson impurity model (AIM)---the central component of DMFT calculations. The key advance is the use of an ensemble error-correction approach to generate fast and accurate solutions of AIM. An example calculation of the Mott transition using DMFT in the single band Hubbard model is given as an example of the technique, and is validated against the most accurate available method. This approach is called data-driven dynamical mean-field theory (${\mathbf{d}}^{3}\mathbf{MFT}$).

arXiv:2107.13960Physical review. B./Physical review. BNov 17, 202119 citations

Dynamical Mean Field Theory

Yoshio Kuramoto

Lecture notes in physicsJan 1, 20200 citations

Machine learning for many-body physics: efficient solution of dynamical mean-field theory

Louis-François Arsenault, O. Anatole von Lilienfeld, Andrew J. Millis

Machine learning methods for solving the equations of dynamical mean-field theory are developed. The method is demonstrated on the three dimensional Hubbard model. The key technical issues are defining a mapping of an input function to an output function, and distinguishing metallic from insulating solutions. Both metallic and Mott insulator solutions can be predicted. The validity of the machine learning scheme is assessed by comparing predictions of full correlation functions, of quasi-particle weight and particle density to values directly computed. The results indicate that with modest further development, machine learning approach may be an attractive computational efficient option for real materials predictions for strongly correlated systems.Machine learning methods for solving the equations of dynamical mean-field theory are developed. The method is demonstrated on the three dimensional Hubbard model. The key technical issues are defining a mapping of an input function to an output function, and distinguishing metallic from insulating solutions. Both metallic and Mott insulator solutions can be predicted. The validity of the machine learning scheme is assessed by comparing predictions of full correlation functions, of quasi-particle weight and particle density to values directly computed. The results indicate that with modest further development, machine learning approach may be an attractive computational efficient option for real materials predictions for strongly correlated systems.

arXiv:1506.08858Jun 29, 201529 citations

Dynamical Mean-Field Theory

Dieter Vollhardt, Krzysztof Byczuk, Marcus Kollar

arXiv:1109.4833Springer series in solid-state sciencesAug 9, 201118 citations

{\mathbf{d}}^{3}\mathbf{MFT}