Entanglement entropy and polarization in the extended long-range non-Hermitian Su-Schrieffer-Heeger model

Abstract Higher winding numbers in topological phases signify more intricate quantum structures, offering enhanced robustness to perturbations by capturing the multiple ways quantum states wrap around parameter space. In this paper, we extend the Su–Schrieffer–Heeger (SSH) model to incorporate fifth-nearest-neighbor hopping and gain/loss imaginary potentials, achieving higher winding numbers and uncovering a richer spectrum of topological phenomena. We show that both the fifth-nearest-neighbor hopping and imaginary potentials significantly influence entanglement entropy and polarization, with both quantities serving as effective indicators of topological phase transitions. Furthermore, we demonstrate that these transitions can also be marked by changes in the bulk band gap and the presence of topologically protected edge states. Notably, we observe the emergence of localized isolated states within the bulk band structure under the influence of non-Hermitian effects, a process that is effectively described by entanglement entropy. These results contribute to a deeper understanding of non-Hermitian topological systems and offer potential insights for the design of novel quantum technologies.