Topological bosonic Bogoliubov excitations with sublattice symmetry

Here we investigate the internal sublattice symmetry, and thus the enriched topological classification of bosonic Bogoliubov excitations of thermodynamically stable free-boson systems with nonvanishing particlenumber-nonconserving terms. Specifically, we show that such systems well described by the bosonic Bogoliubov-de Gennes Hamiltonian can be in general reduced to particle-number-conserving (single-particle) ones. Building upon this observation, the sublattice symmetry is uncovered with respect to an excitation energy, which is usually hidden in the bosonic Bogoliubov-de Gennes Hamiltonian. Thus, we obtain an additional topological class, i.e., class AIII, which enriches the framework for the topological threefold way of free-boson systems. Moreover, a construction is proposed to show a category of systems respecting such a symmetry. For illustration, we resort to a one-dimensional prototypical model to demonstrate the topological excitation characterized by a winding number or symplectic polarization. By introducing the correlation function, we present an approach to measure the topological invariant. In addition, the edge excitation together with its robustness to symmetry-preserving disorders is also discussed.