The bulk-boundary correspondence in one dimension asserts that the physical quantities defined in the bulk and at the edge are connected, as well established in the argument for electric polarization. Recently, a spectral bulk-boundary correspondence (SBBC), an extended version of the conventional bulk-boundary correspondence to energy-dependent spectral functions, such as Greens functions, has been proposed in chiral symmetric systems, in which the chiral operator anticommutes with the Hamiltonian. In this study, we extend the SBBC to a system with impurity scattering and dynamical self-energies, regardless of the presence or absence of a gap in the energy spectrum. Moreover, the SBBC is observed to hold even in a system without chiral symmetry, which substantially generalizes its concept. The SBBC is demonstrated with concrete models, such as superconducting nanowires and a normal metallic chain. Its potential applications and certain remaining issues are also discussed.
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