Time evolution of ML-MCTDH wavefunctions. II. Application of the projector splitting integrator

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• The multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) method is crucial for simulating quantum dynamics.
• Numerical instabilities arise in ML-MCTDH for weakly entangled wavefunctions due to singularities in equations of motion (EOMs).
• Regularization techniques are often required to address these EOM instabilities.

Purpose of the Study:

• To implement and evaluate the multi-layer Projector Splitting Integrator (PSI) for ML-MCTDH.
• To demonstrate the efficiency and stability of PSI compared to standard ML-MCTDH and other regularization methods.
• To assess PSI's performance on challenging multi-spin-boson models with large parameter spaces.

Main Methods:

• Implementation of the multi-layer Projector Splitting Integrator (PSI).
• Comparison of PSI with standard ML-MCTDH and improved regularization schemes.
• Testing on spin-boson models with up to 10^6 bath modes and multi-spin-boson models with up to ~1.3x10^9 parameters.

Main Results:

• PSI provides a singularity-free approach for evolving ML-MCTDH wavefunctions.
• PSI significantly reduces computational cost: 3-4 orders of magnitude fewer Hamiltonian evaluations and 2-3 orders of magnitude fewer applications than standard ML-MCTDH.
• PSI outperforms other regularization schemes, requiring 2-3/1-2 orders of magnitude fewer evaluations/applications, respectively.

Conclusions:

• The multi-layer PSI is an efficient and stable method for large-scale quantum dynamics simulations.
• PSI overcomes numerical instabilities inherent in standard ML-MCTDH, enabling accurate dynamics for complex systems.
• PSI demonstrates superior performance, making it a valuable tool for advanced quantum mechanical calculations.