Decoherence of chiral magnon edge modes in a topological bosonic Chern insulator

Magnonic Chern insulators host chiral edge modes that propagate unidirectionally along system boundaries and are protected against elastic backscattering by the non-zero Chern number. These modes have been observed in several magnetic materials and are promising candidates for low-dissipation spin-transport platforms. A key open question concerns how edge excitations lose coherence when coupled to realistic environmental degrees of freedom. We theoretically analyse decoherence in chiral magnon edge modes of a honeycomb ferromagnet with Dzyaloshinskii-Moriya interactions. Starting from a microscopic spin model, a Holstein-Primakoff expansion is performed and the resulting bosonic Haldane Hamiltonian is derived explicitly. Edge modes in a zigzag ribbon geometry are obtained via exact lattice diagonalisation, and their spatial profiles are used to construct a momentum-resolved open-system description. Within the Born-Markov and secular approximations, a Lindblad master equation is derived and used to compute relaxation, pure dephasing, coherence decay and entanglement loss. The results identify which features of decoherence are constrained by band topology, such as the suppression of elastic backscattering, and which remain sensitive to environmental noise irrespective of the Chern number. Numerical simulations show the dependence of decoherence on momentum, temperature, edge localisation and group velocity, and provide experimentally accessible predictions for coherence times and line-widths. The developed framework provides a unified approach to dissipative dynamics in topological magnonics, bridging microscopic spin-wave theory and open-system formalisms.