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Topological edge states for disordered bosonic systems

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Citation

Peano, V., & Schulz-Baldes, H. (2018). Topological edge states for disordered bosonic systems. Journal of Mathematical Physics, 59(3). doi:10.1063/1.5002094.


Cite as: https://hdl.handle.net/21.11116/0000-0002-A923-8
Abstract
Quadratic bosonic Hamiltonians over a one-particle Hilbert space can be described by a Bogoliubov-de Gennes (BdG) Hamiltonian on a particle-hole Hilbert space. In general, the BdG Hamiltonian is not self-adjoint, but only J-self-adjoint on the particle-hole space viewed as a Krein space. Nevertheless, its energy bands can have non-trivial topological invariants like Chern numbers or winding numbers. By a thorough analysis for tight-binding models, it is proved that these invariants lead to bosonic edge modes which are robust to a large class of possibly disordered perturbations. Furthermore, general scenarios are presented for these edge states to be dynamically unstable even though the bulk modes are stable.