Simple approach to characterizing band topology in bosonic pairing Hamiltonians

We revisit the problem of characterizing band topology in dynamically stable quadratic bosonic Hamiltonians that do not conserve particle number. We show this problem can be rigorously addressed by a smooth and local adiabatic mapping procedure to a particle-number-conserving Hamiltonian. In contrast to a generic fermionic pairing Hamiltonian, such a mapping can always be constructed for bosons. Our approach shows that particle-nonconserving bosonic Hamiltonians can be classified using known approaches for fermionic models. It also provides a simple means for identifying and calculating appropriate topological invariants. We also explicitly study dynamically stable but non-positive-definite Hamiltonians (as arise frequently in driven photonic systems). We show that in this case, each band gap is characterized by two distinct invariants.

Automated summary

The study addresses the characterization of band topology in dynamically stable quadratic bosonic Hamiltonians that do not conserve particle number by mapping them to particle-number-conserving Hamiltonians. It shows that such mapping can always be constructed for bosons, unlike in generic fermionic pairing Hamiltonians. The research also explores the classification of particle-nonconserving bosonic Hamiltonians using known approaches for fermionic models, and provides a straightforward method for identifying and computing appropriate topological invariants.