Twisted XXZ even-chain ground-state conjecture

Let $H^{(N)}$ be the XXZ Hamiltonian with twisted boundary conditions, with $N$ an even number of sites, twisting angle $\phi$, anisotropy $\Delta$, and total spin $z$-axis projection $S_z$. The twisted XXZ even-chain ground-state conjecture. For $\phi=2\pi/3$ and $\Delta=-1/2$, the ground state has energy

$$E=-\frac{3N}{2}$$

and total spin projection $S_z=0$. The statement is presented as the first analogue of the periodic-chain conjectures; the source reports no proof or resolution.