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A new modular tensor diagram approach simplifies constructing spin eigenfunctions for complex fermion systems. This method efficiently organizes the state space and generates universal recursive relations for systems with odd numbers of spins.

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Area of Science:

  • Quantum mechanics
  • Many-body physics
  • Computational physics

Background:

  • Constructing spin eigenfunctions for multi-spin systems becomes complex with increasing system size.
  • A modular tensor diagram approach was previously developed for hierarchical state space decomposition.
  • This approach organizes the state space and constructs symmetry-adapted basis states efficiently.

Purpose of the Study:

  • To generalize the modular tensor diagram approach for fermion systems with odd numbers of spins.
  • To classify elementary modules and map them to geometric building blocks.
  • To generate spin eigenfunctions and universal recursive relations for arbitrary odd-spin systems.

Main Methods:

  • Generalizing the modular tensor diagram approach for odd-spin fermion systems.
  • Classifying elementary modules (primitive spin-pair modules + odd-spin tag module) into module classes.
  • Mapping modules to geometric building blocks to visualize state space structure and symmetry.
  • Generating spin eigenfunctions using symmetry and orthogonality conditions on tagged elementary modules.

Main Results:

  • A generalized modular tensor diagram approach for odd-spin fermion systems.
  • Classification of modules and their mapping to geometric structures.
  • Efficient generation of spin eigenfunctions and universal recursive relations.
  • Exploration of the structure and symmetry of fermion system state spaces.

Conclusions:

  • The generalized approach provides an effectively organized state space for odd-spin fermion systems.
  • This method allows for efficient construction of symmetry-adapted basis states and spin eigenfunctions.
  • The findings offer new insights into quantum many-body systems and spin dynamics.