Small matrix modular path integral: iterative quantum dynamics in space and time.

Area of Science:

• Computational physics
• Quantum chemistry
• Materials science

Background:

• The modular path integral (MPI) formulation is effective for simulating dynamics in one-dimensional extended systems.
• Evaluating spin or exciton-vibration dynamics often requires significant computational resources, scaling with system size.

Purpose of the Study:

• To introduce a novel computational method, small matrix decomposition of the modular path integral (SMatMPI).
• To enable efficient, long-time propagation of dynamics in one-dimensional extended systems.
• To overcome the limitations of tensor storage in existing MPI methods.

Main Methods:

• Development of the small matrix decomposition of the modular path integral (SMatMPI).
• Implementation of SMatMPI for evaluating spin and exciton-vibration dynamics.
• Iterative long-time propagation techniques.

Main Results:

• SMatMPI eliminates the need for large tensor storage, reducing memory requirements.
• The method allows for linear scaling of computational effort with the number of units in the system.
• Successful demonstration of iterative long-time propagation for complex dynamics.

Conclusions:

• SMatMPI offers a computationally efficient and scalable approach for studying quantum dynamics in extended systems.
• This method significantly advances the simulation capabilities for molecular aggregates and spin arrays.
• The technique facilitates deeper insights into exciton-vibration coupling and spin dynamics over extended timescales.