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We propose to experimentally explore the Haldane phase in spin-one XXZantiferromagnetic chains using trapped ions. We show how to adiabaticallyprepare the ground states of the Haldane phase, demonstrate their robustnessagainst sources of experimental noise, and propose ways to detect the Haldaneground states based on their excitation gap and exponentially decayingcorrelations, nonvanishing nonlocal string order, and doubly-degenerateentanglement spectrum.

Simulating the Haldane Phase in Trapped Ion Spins Using Optical Fields