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An efficient method for strongly correlated electrons in two-dimensions.

Ion Mitxelena1, Mario Piris1

  • 1Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU) and Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain.

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|February 17, 2020
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Summary

This study introduces the Piris Natural Orbital Functional 7 (PNOF7) method for strongly correlated electrons in 2D systems. PNOF7 accurately calculates ground-state energies and describes strong correlation effects efficiently, outperforming other methods with reduced computational cost.

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Area of Science:

  • Quantum Chemistry
  • Condensed Matter Physics
  • Computational Materials Science

Background:

  • Strongly correlated electrons in two-dimensional (2D) systems present significant computational challenges.
  • Reduced Density Matrix (RDM) based methods offer a pathway to study these systems.
  • Accurate description of electron correlation is crucial for understanding material properties.

Purpose of the Study:

  • To introduce and validate the Piris Natural Orbital Functional 7 (PNOF7) for strongly correlated 2D electron systems.
  • To assess PNOF7's ability to accurately compute ground-state energies and describe electron correlation.
  • To compare PNOF7's performance against established methods like DMRG and exact diagonalization.

Main Methods:

  • Application of the Piris Natural Orbital Functional 7 (PNOF7) functional.
  • Utilizing natural orbitals and occupation numbers to determine ground-state energy.
  • Studying the 2D Hubbard model and hydrogen square lattices.
  • Investigating singlet ground-states and doublet mixed quantum states.

Main Results:

  • PNOF7 accurately describes strong correlation effects in 2D systems, showing consistent results for various system sizes and fillings.
  • The method satisfies necessary N-representability conditions and conserves total spin.
  • PNOF7 demonstrates computational efficiency, scaling to mean-field cost, and is independent of dimensionality.
  • Long-range correlation effects on electron detachment energies were observed in 2D hydrogen lattices.

Conclusions:

  • PNOF7 is a robust and computationally efficient tool for studying strongly correlated electrons in 2D.
  • The functional provides accurate ground-state energies and reliably describes correlation effects.
  • PNOF7 offers a promising alternative to existing methods, particularly for large and strongly correlated systems.