A simple approach to characterizing band topology in bosonic pairing Hamiltonians

• URL: http://arxiv.org/abs/2104.07449v2
• Date: Tue, 22 Jun 2021 13:55:34 GMT
• Title: A simple approach to characterizing band topology in bosonic pairing Hamiltonians
• Authors: Gaurav Chaudhary, Michael Levin, and Aashish A. Clerk
• Abstract summary: 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. Our approach shows that particle non-conserving bosonic Hamiltonians can be classified using known approaches for fermionic models.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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