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Abstract

We study the Kitaev-Heisenberg Gamma-Gamma model that describes the magnetism in spin-orbit coupled honeycomb lattice Mott insulators. In strong magnetic fields perpendicular to the plane of the lattice ([111] direction) that bring the system into the fully polarized paramagnetic phase, we find that the spin-wave bands carry nontrivial Chern numbers over large regions of the phase diagram, implying the presence of chiral magnon edge states. In contrast to other topological magnon systems, the topological nontriviality of these systems results from the presence of anisotropic terms in the Hamiltonian that do not conserve the number of magnons. Since the effects of interactions are suppressed by the exchange scale divided by the applied field strength, the validity of the single-particle picture is tunable, making paramagnetic phases particularly suitable for the exploration of this physics. Using time-dependent density matrix renormalization group methods and interacting spin-wave theory, we demonstrate the presence of the chiral edge mode and its evolution with field.