Localization Dynamics at the Exceptional Point of Non-Hermitian Creutz Ladder

We propose a quasi-one-dimensional non-Hermitian Creutz ladder with entirely flat spectrum by introducing alternating gain and loss components while maintaining inversion symmetry. Destructive interference generates flat spectrum at the exceptional point, where the Creutz ladder maintains coalesced and degenerate eigenvalues with compact localized states distributed in single plaquette. All excitations are completely confined within the localization area, unaffected by gain and loss. Single-site excitations exhibit nonunitary dynamics with intensities increasing due to level coalescence, while multiple-site excitations may display oscillating or constant intensities at the exceptional point. These results provide insights into the fascinating dynamics of non-Hermitian localization, where level coalescence and degeneracy coexist at the exceptional point.