Symmetries in the multi-configurational time-dependent Hartree wavefunction representation and propagation

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• The multi-configurational time-dependent Hartree (MCTDH) method uses multi-layered wavefunction representations.
• Transformations between equivalent representations can interchange single-particle functions (SPFs) and single-hole functions (SHFs).
• Standard MCTDH equations of motion lack invariance under these transformations, leading to singularities.

Purpose of the Study:

• To develop revised MCTDH equations of motion that are invariant under tree transformations.
• To introduce a new integration scheme that avoids singularities and preserves wavefunction invariance.
• To enhance the numerical stability and accuracy of quantum dynamics simulations.

Main Methods:

• Introducing transformed SPFs that satisfy different normalization conditions.
• Deriving revised equations of motion invariant under tree transformations.
• Developing a novel integration scheme combining existing advantageous approaches.

Main Results:

• The revised equations of motion are invariant under tree transformations.
• The new integration scheme avoids singularities associated with the inverse single-particle density matrix.
• Numerical simulations on the spin boson model demonstrate the scheme's favorable properties.

Conclusions:

• The developed method provides a singularity-free and invariant approach for MCTDH calculations.
• The new integration scheme offers improved numerical stability and accuracy for quantum dynamics.
• This work advances the computational treatment of complex quantum systems.