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Variational wave function are an invaluable tool to study the properties of strongly correlated systems. We propose such a wave function, based on the theory of auxiliary fields and combining aspects of auxiliary-field quantum Monte Carlo and modern variational optimization techniques including automatic differentiation. The resulting , consisting of several slices of optimized projectors, is highly expressive and systematically improvable. We benchmark this form on the two-dimensional Hubbard model, using both cylindrical and large, fully periodic supercells. The computed ground-state energies are competitive with the best variational results. Moreover, the optimized wave functions predict the correct ground-state order with near full symmetry restoration (i.e., translation invariance) despite initial states with incorrect orders. The can become a tool for local order prediction, leading to a new paradigm for variational studies of bulk systems. It can also be viewed as an approach to produce accurate and systematically improvable wave functions in a convenient form of nonorthogonal Slater determinants (e.g., for quantum chemistry) at polynomial computational cost. Published by the American Physical Society 2024
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