Mapped bulk-boundary correspondence in nonlocal systems with strong long-range coupling

Most of the fundamental concepts of topological classification and characterization are based on an assumption of short-range coupling. These cognitions may largely fail for long-range systems with power-law decay exponent $\ensuremath{\beta}$, which have received increasing attention with the fast progress in artificial assembled quantum simulators. Especially, the bulk-boundary correspondence may weaken $(0<\ensuremath{\beta}<1)$ or completely break down $(\ensuremath{\beta}=0)$, cases where the bulk topological invariant alone is insufficient to determine the number of edge modes. Here, we propose a mapped bulk-boundary correspondence to characterize topological edge modes of nonlocal systems with strong long-range coupling $0\ensuremath{\le}\ensuremath{\beta}<1$. The analytic results show that strong long-range hoppings can induce infinitely large topological regions. Our method is also applicable to the Rydberg-dressed systems with an infinite dressing radius.