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Quantification of electron correlation for approximate quantum calculations.

Shunyue Yuan1, Yueqing Chang1, Lucas K Wagner1

  • 1Department of Physics, University of Illinois Urbana-Champaign, Champaign, Illinois 61801, USA.

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This study introduces the von Neumann entropy of the one-particle reduced density matrix (1-RDM) as a new metric for evaluating quantum chemistry methods. This approach enhances the assessment of electron correlation beyond total energy calculations.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Many-Body Physics

Background:

  • State-of-the-art computational methods for solving the many-body Schrödinger equation often employ heuristics for accuracy and efficiency.
  • Total energy is the conventional metric for assessing accuracy, but it offers an incomplete view of electron correlation.

Purpose of the Study:

  • To evaluate the efficacy of the von Neumann entropy of the one-particle reduced density matrix (1-RDM) as a benchmark for quantum chemistry methods.
  • To compare the performance of selected configuration interaction (CI), coupled cluster, variational Monte Carlo, and fixed-node diffusion Monte Carlo techniques.

Main Methods:

  • Assessment of the von Neumann entropy of the 1-RDM for benchmark hydrogen chains.
  • Development and application of a novel algorithm, the circle reject method, to enhance the efficiency of von Neumann entropy evaluation using quantum Monte Carlo.
  • Analysis of the eigenvalues of the 1-RDM.

Main Results:

  • The circle reject method significantly improves the efficiency of von Neumann entropy calculations by several orders of magnitude.
  • The von Neumann entropy of the 1-RDM effectively distinguishes between dynamic and static electron correlation.
  • The study confirms existing hypotheses regarding the differences between selected CI and Slater-Jastrow wave functions.

Conclusions:

  • The von Neumann entropy of the 1-RDM provides a more comprehensive measure of electron correlation than total energy.
  • The developed circle reject method offers a substantial computational advantage for quantum Monte Carlo calculations.
  • This work validates and refines our understanding of electron correlation in various quantum chemistry approaches.