Local Embedding and Effective Downfolding in the Auxiliary-Field Quantum Monte Carlo Method

Area of Science:

• Computational Chemistry
• Condensed Matter Physics
• Quantum Mechanics

Background:

• Auxiliary-field quantum Monte Carlo (AFQMC) is a powerful method for electronic structure calculations.
• Accurate AFQMC calculations are computationally intensive, limiting system sizes.
• Previous local embedding schemes focused only on the occupied electronic sector.

Purpose of the Study:

• To develop and implement a local embedding and effective downfolding scheme within AFQMC.
• To extend the methodology to include the virtual electronic sector for computational efficiency.
• To enable the study of larger and more complex systems using AFQMC.

Main Methods:

• A local cluster with full electron correlation is defined.
• The frozen orbital method constructs an effective Hamiltonian for the local cluster.
• The scheme incorporates effective downfolding of the virtual sector.
• The approximation is controlled by active occupied (R_o) and virtual (R_v) region sizes.

Main Results:

• The new methodology significantly reduces computational effort for AFQMC.
• The feasible system size treatable by AFQMC is greatly extended.
• Systematic investigation shows rapid convergence of energies with R_o and R_v.
• Relative energies converge quickly to the full AFQMC treatment.

Conclusions:

• The developed local embedding and downfolding scheme is effective for AFQMC.
• This approach offers a computationally tractable way to study larger systems.
• The method provides accurate results comparable to full AFQMC calculations.