Detecting topological phase transitions through entanglement between disconnected partitions in a Kitaev chain with long-range interactions

We explore the behaviour of the disconnected entanglement entropy (DEE) across the topological phases of a long range interacting Kitaev chain where the long range interactions decay as a power law with an exponent $\alpha$. We show that while the DEE may not remain invariant deep within the topologically non-trivial phase when $\alpha<1$, it nevertheless shows a quantized discontinuous jump at the quantum critical point and can act as a strong marker for the detection of topological phase transition. We also study the time evolution of the DEE after a sudden quench of the chemical potential within the same phase. In the short range limit of a finite chain, the DEE is expected to remain constant upto a critical time after the quench, which diverges in the thermodynamic limit. However, no such critical time is found to exist when the long range interactions dominate (i.e., $\alpha<1$).