  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-$U$ $SU(2N)$ 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 Moir\'e 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.
