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In conventional Hermitian systems with the open boundary condition, Bloch'stheorem is perturbatively broken down, which means although the crystalmomentum is not a good quantum number, the eigenstates are the superposition ofseveral extended Bloch waves. In this paper, we show that Bloch's theorem canbe non-perturbatively broken down in some Hermitian Bosonic systems. Thequasiparticles of the system are the superposition of localized non-Blochwaves, which are characterized by the complex momentum whose imaginary partdetermines the localization properties. Our work is a Hermitian generalizationof the non-Hermitian skin effect, although they share the same mechanism.

Non-perturbative Breakdown of Bloch's Theorem and Hermitian Skin Effects