We propose a projection approach to perform quantum Monte Carlo (QMC) simulation on the infinite-$U$ Hubbard model 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-$USU\left(2N\right)$ fermionic Hubbard model on both a 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 two-dimensional Moiré 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 $SU\left(2N\right)$ quantum spin models and Kondo lattice models may be studied in the framework of fermionic QMC simulations.

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• Magnetic order
• Quantum spin liquid
• Strongly correlated systems
• Extended Hubbard model
• Hubbard model
• Quantum Monte Carlo