Multi-layer Potfit: an accurate potential representation for efficient high-dimensional quantum dynamics.

Area of Science:

• Quantum dynamics
• Computational chemistry
• Theoretical physics

Background:

• The multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) method is crucial for simulating high-dimensional quantum systems.
• Efficient computation of multi-dimensional matrix elements requires specific Hamiltonian structures.
• Fitting potential energy surfaces (PES) for high-dimensional systems is challenging due to large, unpredictable fits.

Purpose of the Study:

• Introduce a novel fitting scheme, multi-layer Potfit (MLPF), for potential energy surfaces (PES).
• Enable practical and accurate PES representations for high-dimensional quantum systems.
• Reduce the computational burden of ML-MCTDH calculations.

Main Methods:

• Developed the multi-layer Potfit (MLPF) scheme based on hierarchical singular value decomposition.
• Represented PES in the hierarchical tensor (HT) format.
• Derived a recursive scheme for integrating HT-format PES within ML-MCTDH.

Main Results:

• MLPF yields near-optimal PES fits with strict accuracy bounds.
• The use of MLPF reduces the numerical effort for ML-MCTDH by orders of magnitude compared to POTFIT.
• MLPF demonstrates significant computational savings for high-accuracy PES and even for systems with four modes.

Conclusions:

• MLPF offers a practical and accurate solution for PES fitting in high-dimensional quantum dynamics.
• The HT-format PES significantly enhances the efficiency of ML-MCTDH calculations.
• MLPF is particularly advantageous for achieving high accuracy and computational efficiency in quantum simulations.