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Jordan-Wigner Transformation for the Description of Strong Correlation in Fermionic Systems.

Thomas M Henderson1,2, Guo P Chen1, Gustavo E Scuseria1,2

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This study introduces a new method using the Jordan-Wigner transformation to achieve accurate and efficient calculations for strongly correlated systems. It provides high-quality energy and density matrix results at a reduced computational cost.

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Area of Science:

  • Quantum chemistry
  • Computational physics
  • Strongly correlated systems

Background:

  • Seniority is a method for organizing Hilbert space in strongly correlated systems.
  • Doubly Occupied Configuration Interaction (DOCI) offers accurate results but has high computational costs.
  • Pair Coupled Cluster Doubles approximates DOCI energies but can fail and yields poor density matrices.

Purpose of the Study:

  • To develop a polynomial-cost method for calculating accurate energies and density matrices for strongly correlated systems.
  • To adapt the seniority zero problem into a fermionic one using the Jordan-Wigner transformation.
  • To overcome the limitations of existing methods like Pair Coupled Cluster Doubles.

Main Methods:

  • Utilizing the Jordan-Wigner transformation to map seniority zero problems to fermionic ones.
  • Applying mean-field variational approaches to the transformed Hamiltonian.
  • Proving that the Hartree-Fock wave function on the transformed Hamiltonian relates to variational coupled cluster doubles.

Main Results:

  • Achieved DOCI-quality results for energies and density matrices for the Hubbard model and small molecular systems.
  • Demonstrated polynomial computational cost, a significant improvement over combinatorial costs.
  • Showcased protection against collapse, a common issue in such calculations.

Conclusions:

  • The Jordan-Wigner transformation provides an efficient and accurate method for strongly correlated systems.
  • This approach yields reliable energies and density matrices, overcoming limitations of previous methods.
  • The method is robust and applicable to various challenging quantum mechanical problems.