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Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods

Mario Motta1, David M. Ceperley2, Garnet Kin-Lic Chan3, John A. Gomez4, Emanuel Gull5, Sheng Guo3, Carlos A. Jiménez-Hoyos3, Tran Nguyen Lan6,5,*, Jia Li5 et al. (Simons Collaboration on the Many-Electron Problem)

Jia Li5, Fengjie Ma7, Andrew J. Millis8, Nikolay V. Prokof’ev9,10, Ushnish Ray3, Gustavo E. Scuseria4,11, Sandro Sorella12,13, Edwin M. Stoudenmire14, Qiming Sun3, Igor S. Tupitsyn9,10, Steven R. White14, Dominika Zgid6, and Shiwei Zhang1,† (Simons Collaboration on the Many-Electron Problem)

  • 1Department of Physics, College of William and Mary, Williamsburg, Virginia 23187, USA
  • 2Department of Physics, University of Illinois at Urbana-Champaign, Champaign, Illinois 61801, USA
  • 3Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
  • 4Department of Chemistry, Rice University, Houston, Texas 77005, USA
  • 5Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
  • 6Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
  • 7Department of Physics, Beijing Normal University, Beijing, Beijing 100875, China
  • 8Department of Physics, Columbia University, New York, New York 10027, USA
  • 9Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
  • 10National Research Center “Kurchatov Institute,” 123182 Moscow, Russia
  • 11Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
  • 12SISSA-International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, Italy
  • 13Democritos Simulation Center CNR-IOM Istituto Officina dei Materiali, Via Bonomea 265, 34136 Trieste, Italy
  • 14Department of Physics and Astronomy, University of California, Irvine, California 92697-4575, USA

  • *On leave from: Ho Chi Minh City Institute of Physics, VAST, Ho Chi Minh City, Vietnam.
  • †shiwei@wm.edu
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Phys. Rev. X 7, 031059 – Published 28 September, 2017Erratum Phys. Rev. X 11, 029901 (2021)

DOI: https://doi.org/10.1103/PhysRevX.7.031059

Abstract

We present numerical results for the equation of state of an infinite chain of hydrogen atoms. A variety of modern many-body methods are employed, with exhaustive cross-checks and validation. Approaches for reaching the continuous space limit and the thermodynamic limit are investigated, proposed, and tested. The detailed comparisons provide a benchmark for assessing the current state of the art in many-body computation, and for the development of new methods. The ground-state energy per atom in the linear chain is accurately determined versus bond length, with a confidence bound given on all uncertainties.

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Corrections

24 March, 2021

Erratum

Publisher’s Note: Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods [Phys. Rev. X 7, 031059 (2017)]

Mario Motta, David M. Ceperley, Garnet Kin-Lic Chan, John A. Gomez, Emanuel Gull, Sheng Guo, Carlos A. Jiménez-Hoyos, Tran Nguyen Lan, Jia Li, Fengjie Ma, Andrew J. Millis, Nikolay V. Prokof’ev, Ushnish Ray, Gustavo E. Scuseria, Sandro Sorella, Edwin M. Stoudenmire, Qiming Sun, Igor S. Tupitsyn, Steven R. White, Dominika Zgid, and Shiwei Zhang
Phys. Rev. X 11, 029901 (2021)

Popular Summary

One of the grand challenges of modern science is to understand and predict the quantum-mechanical behavior of a large ensemble of interacting electrons. Physical and chemical properties of materials and molecules are often the result of a delicate balance between competing behaviors in a many-electron system. Accurate computations are essential for predicting outcomes, but performing such calculations in a straightforward manner requires unattainable computational expense. Researchers have therefore come up with a variety of theoretical and numerical techniques to work around this hurdle. We present a comprehensive benchmark study of quantum many-body computational methods for addressing this challenge.

Our work focuses on two key aspects in treating real materials: the presence of long-ranged Coulomb interactions (the electrostatic force felt among electrons) and the need to study the continuum and thermodynamic limits. We characterize the relative accuracy and capabilities of 16 methods for performing many-electron calculations, which provides a survey of the state-of-the-art to guide applications. A large amount of data is produced that will be useful in benchmarking other existing and future electronic structure methods. Combining the strengths of complementary methods, we determine the equation of state (energy per atom versus interatomic spacing) of an infinite linear chain of hydrogen atoms in the continuum limit to high accuracy.

Future work can extend these benchmarks to more complex materials. Any progress in addressing the computational challenge of many-electron systems will be fundamental to “materials genome” initiatives, which attempt to discover and design new materials for a range of applications.

Article Text

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  108. For R=1.0 and 1.2aB we perform fragment-size extrapolations on H1200, which is not converged with respect to the full system size. Our extrapolated result includes a full-system correction determined from calculations on larger systems, with a fragment of size [22].

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Phys. Rev. X 7, 031059– Published 28 September, 2017
  • Received 1 May 2017
  • Corrected 24 March 2021
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