%0 Journal Article %J Physical Review B %D 2016 %T Kaleidoscope of quantum phases in a long-range interacting spin-1 chain %A Zhe-Xuan Gong %A Mohammad F. Maghrebi %A Anzi Hu %A Michael Foss-Feig %A Philip Richerme %A Christopher Monroe %A Alexey V. Gorshkov %X Motivated by recent trapped-ion quantum simulation experiments, we carry out a comprehensive study of the phase diagram of a spin-1 chain with XXZ-type interactions that decay as 1/rα, using a combination of finite and infinite-size DMRG calculations, spin-wave analysis, and field theory. In the absence of long-range interactions, varying the spin-coupling anisotropy leads to four distinct phases: a ferromagnetic Ising phase, a disordered XY phase, a topological Haldane phase, and an antiferromagnetic Ising phase. If long-range interactions are antiferromagnetic and thus frustrated, we find primarily a quantitative change of the phase boundaries. On the other hand, ferromagnetic (non-frustrated) long-range interactions qualitatively impact the entire phase diagram. Importantly, for α≲3, long-range interactions destroy the Haldane phase, break the conformal symmetry of the XY phase, give rise to a new phase that spontaneously breaks a U(1) continuous symmetry, and introduce an exotic tricritical point with no direct parallel in short-range interacting spin chains. We show that the main signatures of all five phases found could be observed experimentally in the near future. %B Physical Review B %V 93 %P 205115 %8 2016/05/11 %G eng %U http://arxiv.org/abs/1510.02108 %N 20 %R http://dx.doi.org/10.1103/PhysRevB.93.205115