Topological phases with long-range interactions

Topological phases ofmatter are primarily studied in systems with short-range interactions. In nature, however, nonrelativistic quantum systems often exhibit long-range interactions. Under what conditions topological phases survive such interactions, and how they are modified when they do, is largely unknown. By studying the symmetry-protected topological phase of an antiferromagnetic spin-1 chain with 1/r(alpha) interactions, we show that two very different outcomes are possible, depending on whether or not the interactions are frustrated. While unfrustrated long-range interactions can destroy the topological phase for alpha less than or similar to 3, the topological phase survives frustrated interactions for all alpha > 0. Our conclusions are based on strikingly consistent results from large-scale matrix-product-state simulations and effective-field-theory calculations, and we expect them to hold for more general interacting spin systems. The models we study can be naturally realized in trapped-ion quantum simulators, opening the prospect for experimental investigation of the issues confronted here.