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Updated: Feb 8, 2026

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Benchmarking the Variational Reduced Density Matrix Theory in the Doubly Occupied Configuration Interaction Space

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Summary

Variational reduced density matrix theory accurately models quantum systems using seniority zero subspaces. It achieves high accuracy even with random energies, demonstrating its effectiveness for complex many-body problems.

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Area of Science:

  • Quantum many-body theory
  • Computational physics
  • Condensed matter theory

Background:

  • Variational reduced density matrix (VRDM) theory shows promise for quantum many-body systems.
  • Seniority zero subspace and SU(2) algebra are key for exactly solvable models.
  • Richardson-Gaudin (RG) pairing Hamiltonians offer exactly solvable benchmarks.

Purpose of the Study:

  • To benchmark VRDM theory against exactly solvable RG-Kitaev and reduced BCS Hamiltonians.
  • To assess VRDM accuracy for N-representability conditions in systems of 10-100 particles.
  • To evaluate VRDM performance with random single-particle energies relevant to superconducting grains.

Main Methods:

  • Application of VRDM theory to truncated doubly occupied configuration interaction space (seniority zero).
  • Benchmarking against Richardson-Gaudin-Kitaev and reduced BCS Hamiltonians.
  • Numerical computation of N-representability conditions for varying system sizes.

Main Results:

  • Exact numerical results for N-representability conditions were obtained for both models.
  • VRDM theory demonstrated high accuracy, even when random single-particle energies were introduced.
  • The exactness of the N-representability conditions was lost with random energies, but accuracy remained high.

Conclusions:

  • VRDM theory is a highly accurate method for studying quantum many-body systems, particularly within the seniority zero subspace.
  • The theory maintains significant accuracy even when dealing with less idealized conditions, such as random single-particle energies.
  • This work validates VRDM as a powerful tool for investigating complex physical systems like small superconducting grains.