Fermion Hubbard model on non-bipartite lattices: flux problem, gauge fields and emergent chirality*

On some one dimensional (1D) and 2D non-bipartite lattices, we study both free and Hubbard interacting lattice fermions when there are some magnetic fluxes threaded or appropriate gauge fields coupled. On one hand, 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 with an odd number of sites, the optimal flux is determined to be ±π/2. We prove this conclusion for Hubbard interacting fermions by means of a generalized reflection positivity technique. It can further lead to some applications towards 2D non-bipartite lattices such as triangle and Kagome. At half-filling, the optimal flux pattern on the triangular lattice can be ascertained to be [π/2, π/2]. We find that chirality emerges in these optimal flux states. On the other hand, we verify these conclusions and further study other fillings away from half with the numerical exact diagonalization (ED) method and find that, when it deviates from half-filling, Hubbard interactions can even alter the optimal flux patterns on these lattices.