The multi-configurational time-dependent Hartree approach in optimized second quantization: Imaginary time...

Area of Science:

• Quantum chemistry
• Computational physics
• Theoretical chemistry

Background:

• The multilayer multiconfigurational time-dependent Hartree (MCTDH) method is a powerful tool for simulating quantum dynamics.
• The optimized second quantization representation (oSQR) enhances computational efficiency by using an optimized time-dependent orbital basis.

Purpose of the Study:

• To extend the MCTDH-oSQR approach to include imaginary time propagation.
• To investigate particle number conservation within the MCTDH-oSQR framework, particularly for Bose-Hubbard models.
• To develop novel computational techniques for quantum system simulations.

Main Methods:

• Implementation of imaginary time propagation within the MCTDH-oSQR framework.
• Introduction of a novel gauge operator to facilitate efficient imaginary time propagation.
• Detailed analysis of particle number conservation in MCTDH-oSQR calculations for Bose-Hubbard models.

Main Results:

• Demonstrated the feasibility and efficiency of imaginary time propagation using MCTDH-oSQR.
• Identified key differences between real and imaginary time orbital dynamics.
• Uncovered interesting properties of single-particle functions relevant to particle number conservation.
• Proposed a new tensor contraction scheme leveraging particle number conservation.

Conclusions:

• The MCTDH-oSQR method, enhanced with imaginary time propagation and particle number conservation, offers a more efficient and accurate approach for quantum simulations.
• The developed techniques provide valuable insights into the behavior of quantum systems, particularly those described by Bose-Hubbard models.
• This work lays the foundation for further advancements in computational quantum dynamics.