Accelerating the use of multi-determinant trial wave functions in auxiliary-field quantum Monte Carlo calculations

The trial wave function is used in auxiliary-field quantum Monte Carlo (AFQMC) method to initialize the projection, control the sign/phase problem, and serve as the starting point for back-propagation. Typically a single determinant wave function is used. The computation and memory costs of using multi-determinant trial wave functions tends to grow linearly with the number of Slater determinants. An efficient algorithm is proposed for AFQMC simulations with configuration interaction trial wave functions. Large numbers of Slater determinants can be reached with much smaller memory usage and computation time. Systematic tests can be made by increasing the number of determinants in the trial wave function. Thousands to millions of determinants can be reached in molecular systems. The error from the approximation to control the sign/phase problem often becomes negligible with the new capability, and the Monte Carlo fluctuation can be much reduced. We illustrate this with examples on atoms and molecules, including challenging transition metal systems.