Non-Local Phase Transitions in Synthetic Dimensions

Recent cold-atom experiments using internal atomic states as a synthetic dimension have successfully realized an integer quantum Hall state. A natural next step is the realization of a fractional quantum Hall (FQH) phase. In this work, we investigate the stability of FQH–like states in the presence of the anisotropic and non-local interactions intrinsic to synthetic dimension systems. Using Tree Tensor Network simulations, we find that such interactions cause a topological phase transition to a trivial density-wave phase without closing the many-body gap. We demonstrate that synthetic-dimension interactions are a powerful tool to probe the connection between locality and topological order, revealing new pathways to engineer correlated topological matter.