  We propose the $\pi$ flux triangular lattice Hubbard model ($\pi$-THM) as a
prototypical setup to stabilize magnetically disordered quantum states of
matter in the presence of charge fluctuations. The quantum paramagnetic domain
of the $\pi$-THM which we identify for intermediate Hubbard U is framed by a
Dirac semi-metal for weak coupling and by 120${}^{\circ}$ N\'eel order for
strong coupling. Generalizing the Klein duality from spin Hamiltonians to
tight-binding models, the $\pi$-THM maps to a Hubbard model which corresponds
to the $(J_H, J_K)=(-1,2)$ Heisenberg-Kitaev model in its strong coupling
limit. The $\pi$-THM provides a promising microscopic testing ground for exotic
finite-U spin liquid ground states amenable to numerical investigation.
