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

TL;DR

This paper introduces a projection method for quantum Monte Carlo simulations of the infinite-U Hubbard model, revealing cases with sign problem free or algebraic sign structures, enabling efficient study of complex correlated systems.

Contribution

The authors develop a projection approach that allows sign problem free or algebraic sign structure QMC simulations for certain infinite-U Hubbard models and their extensions.

Findings

Sign problem free at half-filling on square and honeycomb lattices.

Algebraic sign structure observed at certain non-half-integer fillings.

Method can be extended to study spin models and Kondo lattice models.

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.