A simple approach to characterizing band topology in bosonic pairing Hamiltonians

TL;DR

This paper introduces a method to classify and analyze the topology of bosonic pairing Hamiltonians by mapping them to particle number conserving models, enabling the use of existing topological invariants.

Contribution

It provides a rigorous adiabatic mapping procedure for bosonic Hamiltonians, allowing their topological classification using fermionic approaches, which was previously challenging.

Findings

Mapping exists for all bosonic pairing Hamiltonians.

Topological invariants can be computed using known fermionic methods.

In non-positive definite cases, each band gap has two invariants.

Abstract

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 non-conserving 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.