Topological classification of excitations in quadratic bosonic systems

We investigate the topological classification of excitations in quadratic bosonic systems with an excitation band gap. Time-reversal, charge-conjugation, and parity symmetries in bosonic systems are introduced to realize a ten-fold symmetry classification. We find a specific decomposition of the quadratic bosonic Hamiltonian and use it to prove that each quadratic bosonic system is homotopic to a direct sum of two single-particle subsystems. The topological classification table is thus derived via inheriting from that of Atland–Zirnbauer classes and unique topological phases of bosons are predicted. Finally, concrete topological models are proposed to demonstrate the peculiarity of bosonic excitations. (paper)