Modular path integral for discrete systems with non-diagonal couplings

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.