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

TL;DR

This paper investigates the effects of magnetic fluxes and gauge fields on non-bipartite lattice fermions, revealing optimal flux patterns, emergent chirality, and non-Fermi liquid features driven by Hubbard interactions.

Contribution

It provides exact results for optimal flux configurations and emergent chirality in non-bipartite lattices using reflection positivity and numerical methods.

Findings

Optimal flux at half-filling on odd-site rings is ±π/2.

Optimal flux patterns on triangular and Kagome lattices are identified.

Hubbard interactions can change flux patterns away from half-filling.

Abstract

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 $\pm{\pi}/2$. 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 $\pm[{\pi}/2,{\pi}/2]$, $\pm[{\pi}/2,{\pi}/2,0]$, 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.