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We investigate the role of disorder on the various topological magnonicphases present in deformed honeycomb ferromagnets. To this end, we introduce abosonic Bott index to characterize the topology of magnon spectra in finite,disordered systems. The consistency between the Bott index and Chern number isnumerically established in the clean limit. We demonstrate that topologicallyprotected magnon edge states are robust to moderate disorder and, asanticipated, localized in the strong regime. We predict a disorder-driventopological phase transition, a magnonic analog of the "topological Andersoninsulator" in electronic systems, where the disorder is responsible for theemergence of the nontrivial topology. Combining the results for the Bott indexand transport properties, we show that bulk-boundary correspondence holds fordisordered topological magnons. Our results open the door for research ontopological magnonics as well as other bosonic excitations in finite anddisordered systems.

Bosonic Bott Index and Disorder-Induced Topological Transitions of Magnons