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This study extends modular path integral decomposition for accurate simulations of complex quantum systems. The method achieves linear scaling, enabling efficient analysis of systems with non-diagonalizable Hamiltonians.

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Area of Science:

  • Quantum mechanics
  • Computational chemistry
  • Theoretical physics

Background:

  • Path integral methods are crucial for simulating quantum systems.
  • Linear scaling algorithms are needed for large systems.
  • Simulating systems with non-diagonalizable Hamiltonians is challenging.

Purpose of the Study:

  • To extend modular path integral decomposition to Hamiltonians with non-diagonalizable intermonomer couplings.
  • To develop an accurate and efficient algorithm for quantum system simulations.
  • To minimize path integral variables while preserving detailed balance.

Main Methods:

  • Modular decomposition of the path integral.
  • Optimal factorization of the time evolution operator.
  • Tensor factorization of the path linking process.

Main Results:

  • Achieved linear scaling with system length.
  • Minimized path integral variables for efficiency.
  • Ensured high accuracy and preservation of detailed balance.
  • Successfully applied to coupled spins and Frenkel exciton chains.

Conclusions:

  • The extended modular path integral decomposition is a powerful tool for simulating complex quantum systems.
  • The method offers significant computational advantages over traditional approaches.
  • This work paves the way for more accurate and efficient simulations in quantum chemistry and physics.