Blog
About

0
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Artificial neural networks for density-functional optimizations in fermionic systems

      , ,

      Scientific Reports

      Nature Publishing Group UK

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          In this work we propose an artificial neural network functional to the ground-state energy of fermionic interacting particles in homogeneous chains described by the Hubbard model. Our neural network functional was proven to have an excellent performance: it deviates from numerically exact calculations by less than 0.15% for a vast regime of interactions and for all the regimes of filling factors and magnetizations. When compared to analytical functionals, the neural functional was found to be more precise for all the regimes of parameters, being particularly superior at the weakly interacting regime: where the analytical parametrization fails the most, ~7%, against only ~0.1% for the neural network. We have also applied our homogeneous functional to finite, localized impurities and harmonically confined systems within density-functional theory (DFT) methods. The results show that while our artificial neural network approach is substantially more accurate than other equivalently simple and fast DFT treatments, it has similar performance than more costly DFT calculations and other independent many-body calculations, at a fraction of the computational cost.

          Related collections

          Most cited references 33

          • Record: found
          • Abstract: not found
          • Article: not found

          Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension

           Elliott Lieb,  F. Wu (1968)
            Bookmark
            • Record: found
            • Abstract: found
            • Article: found
            Is Open Access

            The density-matrix renormalization group

            The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. This algorithm has achieved unprecedented precision in the description of one-dimensional quantum systems. It has therefore quickly acquired the status of method of choice for numerical studies of one-dimensional quantum systems. Its applications to the calculation of static, dynamic and thermodynamic quantities in such systems are reviewed. The potential of DMRG applications in the fields of two-dimensional quantum systems, quantum chemistry, three-dimensional small grains, nuclear physics, equilibrium and non-equilibrium statistical physics, and time-dependent phenomena is discussed. This review also considers the theoretical foundations of the method, examining its relationship to matrix-product states and the quantum information content of the density matrices generated by DMRG.
              Bookmark
              • Record: found
              • Abstract: found
              • Article: found
              Is Open Access

              Density-functionals not based on the electron gas: Local-density approximation for a Luttinger liquid

              By shifting the reference system for the local-density approximation (LDA) from the electron gas to other model systems one obtains a new class of density functionals, which by design account for the correlations present in the chosen reference system. This strategy is illustrated by constructing an explicit LDA for the one-dimensional Hubbard model. While the traditional {\it ab initio} LDA is based on a Fermi liquid (the electron gas), this one is based on a Luttinger liquid. First applications to inhomogeneous Hubbard models, including one containing a localized impurity, are reported.
                Bookmark

                Author and article information

                Contributors
                vivian.franca@unesp.br
                Journal
                Sci Rep
                Sci Rep
                Scientific Reports
                Nature Publishing Group UK (London )
                2045-2322
                13 February 2019
                13 February 2019
                2019
                : 9
                Affiliations
                ISNI 0000 0001 2188 478X, GRID grid.410543.7, Institute of Chemistry, , São Paulo State University, UNESP, ; 14800-090 Araraquara, São Paulo Brazil
                Article
                37999
                10.1038/s41598-018-37999-1
                6374439
                30760812
                © The Author(s) 2019

                Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

                Funding
                Funded by: FundRef https://doi.org/10.13039/501100003593, Ministry of Science, Technology and Innovation | Conselho Nacional de Desenvolvimento Científico e Tecnológico (National Council for Scientific and Technological Development);
                Award ID: 448220/2014-8
                Award Recipient :
                Categories
                Article
                Custom metadata
                © The Author(s) 2019

                Uncategorized

                Comments

                Comment on this article