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

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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Plain Language 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.