@article {1191, title = {Topological phases with long-range interactions}, journal = {Physical Review B}, volume = {93}, year = {2016}, month = {2016/01/08}, pages = {041102}, abstract = { Topological phases of matter are primarily studied in quantum many-body systems with short-range interactions. Whether various topological phases can survive in the presence of long-range interactions, however, is largely unknown. Here we show that a paradigmatic example of a symmetry-protected topological phase, the Haldane phase of an antiferromagnetic spin-1 chain, surprisingly remains intact in the presence of arbitrarily slowly decaying power-law interactions. The influence of long-range interactions on the topological order is largely quantitative, and we expect similar results for more general systems. Our conclusions are based on large-scale matrix-product-state simulations and two complementary effective-field-theory calculations. The striking agreement between the numerical and analytical results rules out finite-size effects. The topological phase considered here should be experimentally observable in a recently developed trapped-ion quantum simulator. }, doi = {10.1103/PhysRevB.93.041102}, url = {http://arxiv.org/abs/1505.03146}, author = {Zhe-Xuan Gong and Mohammad F. Maghrebi and Anzi Hu and Michael L. Wall and Michael Foss-Feig and Alexey V. Gorshkov} }