Self-Refinement of Auxiliary-Field Quantum Monte Carlo via Non-Orthogonal Configuration Interaction.

Area of Science:

• Computational Chemistry
• Quantum Many-Body Physics
• Electronic Structure Theory

Background:

• Auxiliary-field quantum Monte Carlo (AFQMC) is a powerful method for electronic structure calculations.
• Optimal accuracy in AFQMC necessitates trial states composed of multiple Slater determinants.
• Current methods for selecting these determinants can be computationally expensive or indirect.

Purpose of the Study:

• To develop an efficient, in-situ algorithm for selecting Slater determinants within the AFQMC random walk.
• To improve the accuracy and reduce the bias and variance of AFQMC calculations.
• To enable accurate calculations for systems with static correlation or strong spin contamination.

Main Methods:

• An efficient algorithm was developed to select determinants directly from an AFQMC random walk.
• Determinants were included in the trial state based on their contribution to the nonorthogonal configuration interaction energy.
• The refined trial states were used to perform phaseless and free-projection AFQMC calculations.

Main Results:

• The refined trial wave functions significantly reduced phaseless bias and sampling variance.
• AFQMC errors were lowered by up to a factor of 10 for challenging second-row elements.
• Chemical accuracy was achieved for the HEAT set and for benzene, a strongly correlated system.
• A 10-fold increase in the time to solution was observed for benzene due to the increased number of determinants.

Conclusions:

• The developed algorithm provides an efficient way to construct high-quality trial states for AFQMC.
• Improved trial states are crucial for overcoming phaseless errors in systems with static correlation.
• This work enables stable and accurate free-projection AFQMC calculations even in the strongly correlated regime.