  A proposal to use trapped ions to simulate spin-one XXZ antiferromagnetic
(AFM) chains as an experimental tool to explore the Haldane phase is presented.
We explain how to reach the Haldane phase adiabatically, demonstrate the
robustness of the ground states to noise in the magnetic field and Rabi
frequencies, and propose a way to detect them using their characterizations: an
excitation gap and exponentially decaying correlations, a nonvanishing nonlocal
string order and a double degenerate entanglement spectrum. Scaling up to
higher dimensions and more frustrated lattices, we obtain richer phase
diagrams, and we can reach spin liquid phase, which can be detected by its
entanglement entropy which obeys the boundary law.
