  Analog quantum simulation based on ultracold atoms in optical lattices has
catalyzed significant breakthroughs in the study of quantum many-body systems.
These simulations rely on the statistical sampling of electronic Fock states,
which are not easily accessible in classical algorithms. In this work, we
modify the determinantal quantum Monte Carlo by integrating a Fock-state update
mechanism alongside the auxiliary field. This method enables efficient sampling
of Fock-state configurations. The Fock-state restrictive sampling scheme
further enables the pre-selection of multiple ensembles at no additional
computational cost, thereby broadening the scope of simulation to more general
systems and models. Employing this method, we analyze static correlations of
the Hubbard model up to the fourth order and achieve quantitative agreement
with cold-atom experiments. The simulations of dynamical spectroscopies of the
Hubbard and Kondo-lattice models further demonstrate the reliability and
advantage of this method.
