Topological phases with long range interactions.
Topological phases of matter 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 a 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 a 3, the topological phase survives frustrated interactions for all a 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.
Physical review. B