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We propose a projection approach to perform quantum Monte Carlo (QMC)simulation on the infinite-$U$ Hubbard model at some integer fillings whereeither it is sign problem free or surprisingly has an algebraic sign structure-- a power law dependence of average sign on system size. We demonstrate ourscheme on the infinite-$U$ $SU(2N)$ fermionic Hubbard model on both a squareand honeycomb lattice at half-filling, where it is sign problem free, andsuggest possible correlated ground states. The method can be generalized tostudy certain extended Hubbard models applying to cluster Mott insulators ortwo-dimensional Moir\'e systems; among one of them at certain non-half-integerfilling, the sign has an algebraic behavior such that it can be numericallysolved within a polynomial time. Further, our projection scheme can also begeneralized to implement the Gutzwiller projection to spin basis such that$SU(2N)$ quantum spin models and Kondo lattice models may be studied in theframework of fermionic QMC simulations.

Projection of Infinite-$U$ Hubbard Model and Algebraic Sign Structure