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

Yunqing Ouyang; Xiao Yan Xu

doi:10.1103/physrevb.104.l241104

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arXiv · 2108.04832

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

Yunqing Ouyang·Xiao Yan Xu

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Abstract

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.

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Yunqing Ouyang, Xiao Yan Xu. 2021-08-10. Projection of Infinite-$U$ Hubbard Model and Algebraic Sign Structure. https://doi.org/10.1103/physrevb.104.l241104

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