Title: Sampling Electronic Fock States using Determinantal Quantum Monte Carlo

Abstract: 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.