Projection of infinite- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>U</mml:mi></mml:math> Hubbard model and algebraic sign structure

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 structure -- power law dependence of average system size. demonstrate our scheme $SU(2N)$ fermionic both square and honeycomb lattice half-filling, free, suggest possible correlated ground states. The method can be generalized study certain extended models applying cluster Mott insulators two-dimensional Moir\'e systems; among one them non-half-integer filling, behavior such that numerically solved within polynomial time. Further, also implement Gutzwiller spin basis Kondo may studied in framework QMC simulations.