Topological Classification of Excitations in Quadratic Bosonic Systems

Abstract

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.

arXiv comment8pages, 3 tables, 1 figure

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Cited by in corpus (14)

• Programmable quantum simulations of bosonic systems with trapped ions
• Giant spin Nernst effect in a two-dimensional antiferromagnet due to magnetoelastic coupling-induced gaps and interband transitions between magnon-like bands
• Interaction induced topological Bogoliubov excitations in a spin-orbit coupled Bose-Einstein condensate
• Intrinsic Anomalous Hall Effect in a Bosonic Chiral Superfluid
• Subradiant edge states in an atom chain with waveguide-mediated hopping
• Squeezing-induced Topological Gap Opening on Bosonic Bogoliubov Excitations
• Supersymmetry on the lattice: Geometry, Topology, and Flat Bands
• Quantum geometry of bosonic Bogoliubov quasiparticles
• Krein-unitary Schrieffer-Wolff transformation and band touchings in bosonic Bogoliubov-de Gennes and other Krein-Hermitian Hamiltonians
• Topological classifications of quadratic bosonic excitations in closed and open systems with examples
• Topological bosonic Bogoliubov excitations with sublattice symmetry
• Bosonic Weyl excitations induced by $p$-orbital interactions in a cubic optical lattice
• Bosonic Holes in Quadratic Bosonic Systems
• Proof of bulk-edge correspondence for band topology by Toeplitz algebra