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Spin-adapted matrix product states and operators.

Sebastian Keller1, Markus Reiher1

  • 1ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland.

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Summary

Matrix product states (MPSs) and operators (MPOs) offer an alternative to White's density matrix renormalization group algorithm. This study shows how to leverage non-abelian spin symmetry in MPSs and MPOs using the Wigner-Eckart theorem for quantum chemistry.

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Area of Science:

  • Quantum Many-Body Physics
  • Computational Chemistry

Background:

  • Matrix product states (MPSs) and matrix product operators (MPOs) provide a powerful framework for simulating quantum systems.
  • The density matrix renormalization group (DMRG) algorithm, introduced by White, is a key numerical method in this field.
  • Exploiting symmetries can significantly enhance the efficiency of quantum many-body calculations.

Purpose of the Study:

  • To demonstrate the application of non-abelian spin symmetry within the MPS and MPO formalism.
  • To show how the Wigner-Eckart theorem can be utilized to simplify calculations involving spin symmetry.
  • To apply these concepts to the spin-adapted quantum chemical Hamiltonian operator.

Main Methods:

  • Formulation of matrix product states (MPSs) and matrix product operators (MPOs).
  • Application of the Wigner-Eckart theorem for exploiting non-abelian spin symmetry.
  • Development of spin-adapted quantum chemical Hamiltonian operators within the MPS/MPO framework.

Main Results:

  • A method for incorporating non-abelian spin symmetry into MPS and MPO representations is presented.
  • The Wigner-Eckart theorem is shown to be effective in simplifying the treatment of spin symmetry in this context.
  • The developed approach is demonstrated on the spin-adapted quantum chemical Hamiltonian.

Conclusions:

  • The integration of non-abelian spin symmetry with MPSs and MPOs offers a more efficient computational approach.
  • This method provides a pathway for more accurate and scalable quantum chemical calculations.
  • The Wigner-Eckart theorem is a crucial tool for harnessing spin symmetry in tensor network methods.