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Variational wave function ansatze are an invaluable tool to study theproperties of strongly correlated systems. We propose such a wave function,based on the theory of auxiliary fields and combining aspects ofauxiliary-field quantum Monte Carlo and modern variational optimizationtechniques including automatic differentiation. The resulting ansatz,consisting of several slices of optimized projectors, is highly expressive andsystematically improvable. We benchmark this form on the two-dimensionalHubbard model, using both cylindrical and large, fully periodic supercells. Thecomputed ground-state energies are competitive with the best variationalresults. Moreover, the optimized wave functions predict the correctground-state order with near full symmetry restoration (i.e. translationinvariance) despite initial states with incorrect orders. The ansatz can becomea tool for local order prediction, leading to a new paradigm for variationalstudies of bulk systems. It can also be viewed as an approach to produceaccurate and systematically improvable wave functions in a convenient form ofnon-orthogonal Slater determinants (e.g., for quantum chemistry) at polynomialcomputational cost.

Automatic Order Detection and Restoration Through Systematically Improvable Variational Wave Functions