Non-Bloch band theory in bosonic Bogoliubov-de Gennes systems

Abstract

In recent research, it has been shown that non-Hermitian systems exhibit sensitivity to boundaries, and it is caused by the non-Hermitian skin effect. In this work, we construct the non-Bloch band theory in bosonic Bogoliubov--de Gennes (BdG) systems. From our theory, we can calculate the generalized Brillouin zone and the energy spectrum in such systems with open boundary conditions in the thermodynamic limit, and we can thus discuss its non-Hermitian nature, despite Hermiticity of an original Hamiltonian. In fact, we find that the bosonic Kitaev-Majorana chain exhibits rich aspects of the non-Hermitian skin effect, such as instability against infinitesimal perturbations and reentrant behavior, in terms of the non-Bloch band theory. This result indicates that our theory is powerful tool for studying non-Hermitian nature in bosonic BdG systems.

arXiv comment9 pages, 3 figures

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• Optomechanical realization of the bosonic Kitaev-Majorana chain
• Non-Hermitian band topology with generalized inversion symmetry
• Non-Hermitian waves in a continuous periodic model and application to photonic crystals
• Universal competitive spectral scaling from the critical non-Hermitian skin effect
• Symmetry and topological classification of Floquet non-Hermitian systems
• Connections between the Open-boundary Spectrum and Generalized Brillouin Zone in Non-Hermitian Systems
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• Quantum-Squeezing-Induced Point-Gap Topology and Skin Effect
• Amplification of quantum signals by the non-Hermitian skin effect
• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
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