The repulsive fermionic Hubbard model is a typical model describing correlated electronic systems. Although it is a simple model with only a kinetic term and a local interaction term, their competition generates rich phases. When the interaction part is significant, usually in many strongly correlated, flat or narrow band systems, lots of novel correlated phases may emerge. One way to understand the possible correlated phases is to go beyond finite interaction and solve the infinite-$U$ Hubbard model. Solving infinite-$U$ Hubbard model is usually extremely hard, and a large-scale unbiased numerical study is still missing. In this Letter, we propose a projection approach, such that a controllable quantum Monte Carlo (QMC) simulation on infinite-$U$ Hubbard model may be done at some integer fillings where either it is sign problem free or surprisingly has an algebraic sign structure -- a power law dependence of average sign on system size. We demonstrate our scheme on the infinite-$U$ $SU(2N)$ fermionic Hubbard model on both square and honeycomb lattice at half-filling, where it is sign problem free, and suggest possible correlated ground states. The method can be generalized to study certain extended Hubbard models applying to cluster Mott insulators or 2D Morie systems, among one of them at certain non-half integer filling, the sign has an algebraic behavior such that it can be numerically solved within a polynomial time. Further, our projection scheme can also be generalized to implement the Gutzwiller projection to spin basis such that $SU(2N)$ quantum spin models and Kondo lattice models may be studied in the framework of fermionic QMC simulations.
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