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We explore the formation and collective modes of Bose-Einstein condensate ofDirac magnons (Dirac BEC). While we focus on two-dimensional Dirac magnons, anemployed approach is general and could be used to describe Bose-Einsteincondensates with linear quasiparticle spectrum in various systems. By using aphenomenological multicomponent model of pumped boson population together withbosons residing at Dirac nodes, the formation and time evolution of condensatesof Dirac bosons is investigated. The condensate coherence and itsmulticomponent nature are manifested in the Rabi oscillations whose period isdetermined by the gap in the spin-wave spectrum. A Dirac nature of thecondensates could be also probed by the spectrum of collective modes. It isshown that the Haldane gap provides an efficient means to tune between thegapped and gapless collective modes as well as controls their stability.

Bose-Einstein condensate of Dirac magnons: Pumping and collective modes