Abstract: We studied the entanglement entropy and its scaling laws on the one-dimensional non-Hermitian Su-Schrieffer-Heeger model with long-range next-next-nearest hopping. The next-next-nearest hopping leads to the appearance of the topological phase with winding number 2, and the critical points on phase boundaries are also divided into different categories. Based on this, we calculated the central charge of these critical systems using the scaling laws of entanglement entropy. The study on the generalized Brillouin zone demonstrates the self-intersection phenomenon of both energy spectra and generalized Brillouin zones induced by the next-next-nearest hopping, and the results reveal that the bulk-boundary correspondence could still be restored.

Key words: entanglement entropy, generalized Brillouin zone, non-Hermitian skin effect, quantum critical system