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

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.

Published version, 34 pages, 11 figures

References in corpus (12)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• An exact chiral spin liquid with non-Abelian anyons
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Projected wave function study of Z2 spin liquids on the kagome lattice for the spin-1/2 quantum Heisenberg antiferromagnet
• Gapless spin liquids on the three dimensional hyper-kagome lattice of Na${}_4$Ir${}_3$O${}_8$
• Charged fermions coupled to ${\mathbb{Z}}_2$ gauge fields: Superfluidity, confinement and emergent Dirac fermions
• Variational Monte Carlo study of chiral spin liquid in the extended Heisenberg model on the Kagome lattice
• Fermionic spinon theory of square lattice spin liquids near the Néel state
• Quantum paramagnet in a $\pi$ flux triangular lattice Hubbard model
• Emergent U(1) gauge theory with fractionalized boson/fermion from the bose condensation of exciton in multi-band insulator

Cited by in corpus (1)

• Exotic Superfluid with Emergent flux in a one-dimensional Bose-Fermi mixture