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Quantum Monte Carlo (QMC) methods are one of the most important tools forstudying interacting quantum many-body systems. The vast majority of QMCcalculations in interacting fermion systems require a constraint to control thesign problem. The constraint involves an input trial wave function whichrestricts the random walks. We introduce a systematically improvable constraintwhich relies on the fundamental role of the density or one-body density matrix.An independent-particle calculation is coupled to an auxiliary-field QMCcalculation. The independent-particle solution is used as the constraint inQMC, which then produces the input density or density matrix for the nextiteration. The constraint is optimized by the self-consistency between themany-body and independent-particle calculations. The approach is demonstratedin the two-dimensional Hubbard model by accurately determining the ground statewhen collective modes separated by tiny energy scales are present in themagnetic and charge correlations. Our approach also provides an ab initio wayto predict effective interaction parameters for independent-particlecalculations.

physical review. b./physical review. b

Coupling quantum Monte Carlo and independent-particle calculations:  self-consistent constraint for the sign problem based on density or density  matrix