Topological edge states for disordered bosonic systems
Mathematical Physics
2018-04-04 v1 math.MP
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 selfadjoint, but only -selfadjoint 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.
Cite
@article{arxiv.1708.08798,
title = {Topological edge states for disordered bosonic systems},
author = {Vittorio Peano and Hermann Schulz-Baldes},
journal= {arXiv preprint arXiv:1708.08798},
year = {2018}
}