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Fermi-Hubbard model on non-bipartite lattices: flux problem and emergent chirality

On several one-dimensional (1D) and 2D nonbipartite lattices, we study both free and Hubbard interacting lattice fermions when some magnetic fluxes are threaded or gauge fields coupled. First, we focus on finding out the optimal flux which minimizes the energy of fermions at specific fillings. For spin-$1/2$ fermions at half-filling on a ring lattice consisting of odd-numbered sites, the optimal flux turns out to be $\pmπ/2$. We prove this conclusion for Hubbard interacting fermions utilizing a generalized reflection positivity technique, which can lead to further applications on 2D nonbipartite lattices such as triangular and Kagome. At half-filling the optimal flux patterns on the triangular and Kagome lattice are ascertained to be $\pm[π/2,π/2]$, $\pm[π/2,π/2,0]$, respectively (see the meaning of these notations in the main text). We also find that chirality emerges in these optimal flux states. Then, we verify these exact conclusions and further study some other fillings with the numerical exact diagonalization method. It is found that when it deviates from half-filling, Hubbard interactions can alter the optimal flux patterns on these lattices. Moreover, numerically observed emergent flux singularities driven by strong Hubbard interactions in the ground states, both in 1D and 2D, are discussed and interpreted as some kind of non-Fermi liquid feature.