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The computational demand posed by applying multi-Slater determinant trials inphaseless auxiliary-field quantum Monte Carlo methods (MSD-AFQMC) isparticularly significant for molecules exhibiting strong correlations. Here, wepropose using direct-product wave functions as trials for MSD-AFQMC, aiming toreduce computational overhead by leveraging the compactness of multi-Slaterdeterminant trials in direct-product form (DP-MSD). This efficiency arises whenthe active space can be divided into non-coupling subspaces, a condition weterm ``decomposable active space''. By employing localized-active spaceself-consistent field wave functions as an example of such trials, wedemonstrate our proposed approach across a range of molecular systems, eachexhibiting varying degrees of complexity in their electronic structures. Ourfindings indicate that the compact DP-MSD trials can reduce computational costssubstantially, by up to 36 times for the C2H6N4 molecule where the two doublebonds between nitrogen N=N are clearly separated by a C-C single bond, whilemaintaining accuracy when active spaces are decomposable. In the case of largersystems such as the benzene dimer, characterized by weak coupling between thetwo monomers, we observed a decrease in computational cost compared to using acomplete active space trial, yet we retained the same level of accuracy.However, for systems where these active subspaces strongly couple, a scenariowe refer to as "strong subspace coupling", the method's accuracy decreasescompared to that achieved with a complete active space approach. We anticipatethat our method will be beneficial for systems with non-coupling toweakly-coupling subspaces that require local multireference treatments.

Scalable Quantum Monte Carlo with Direct-Product Trial Wave Functions