Abstract
The Bernard-LeClair (BL) symmetry classes generalize the Altland-Zirnbauer classes in the absence of Hermiticity. Within the BL scheme, time-reversal and particle-hole symmetry come in two flavors, and “pseudo-Hermiticity” generalizes Hermiticity. We propose that these symmetries are relevant for the topological classification of non-Hermitian single-particle Hamiltonians and Hermitian bosonic Bogoliubov–de Gennes (BdG) models. We show that the spectrum of any Hermitian bosonic BdG Hamiltonian is found by solving for the eigenvalues of a non-Hermitian matrix which belongs to one of the BL classes. We therefore suggest that bosonic BdG Hamiltonians inherit the topological properties of a non-Hermitian symmetry class and explore the consequences by studying symmetry-protected edge instabilities in a one-dimensional system.
- Received 27 June 2018
DOI:https://doi.org/10.1103/PhysRevB.98.115135
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