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SCF Framework, HF Stability, and RPA Correlation for Jordan-Wigner-Transformed Spin Hamiltonians on Arbitrary

Shadan Ghassemi Tabrizi1,2, Thomas M Henderson3,4, Thomas D Kühne1,2

  • 1Computational System Sciences, Technische Universität Dresden, 01187Dresden, Germany.

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|April 24, 2026
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Summary
This summary is machine-generated.

We developed a new self-consistent field scheme for strongly correlated spin systems using the Jordan-Wigner transformation. This method improves mean-field accuracy for models like XXZ and J1-J2, enhancing computational efficiency.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Systems
  • Computational Physics

Background:

  • Mean-field theories like Hartree-Fock (HF) are effective for strongly correlated spin systems via Jordan-Wigner (JW) transformation.
  • Previous limitations concerning nonlocal JW strings and site ordering have been overcome by absorbing string operators into Thouless rotations.

Purpose of the Study:

  • To develop a novel self-consistent field (SCF) scheme for calculating mean-field energies.
  • To provide an alternative to gradient-based optimization of Thouless parameters.
  • To enhance the accuracy of mean-field descriptions for quantum spin systems.

Main Methods:

  • Developed an SCF scheme expressing mean-field energy as a functional of the single-particle density matrix.
  • Derived the analytical orbital Hessian for diagnosing HF stability.
  • Computed ground-state correlation energy using the random-phase approximation (RPA).

Main Results:

  • The new SCF scheme offers an alternative to traditional optimization methods.
  • HF stability can be diagnosed using the derived analytical orbital Hessian.
  • Random-phase approximation (RPA) significantly improves mean-field accuracy for benchmark models.

Conclusions:

  • The developed SCF approach provides an efficient and accurate method for strongly correlated spin systems.
  • RPA calculations demonstrably enhance the predictive power of mean-field theory.
  • This work offers a robust framework for studying complex quantum magnetism.