Fluctuation-induced first-order phase transitions in the Kitaev-like d4 honeycomb magnet

We study numerically a bosonic analog of the Kitaev honeycomb model, which is a minimal model for $4{d}⁴/5{d}⁴$ quantum magnets with honeycomb lattice geometry. We construct its phase diagram by a combination of Landau theory analysis and quantum Monte Carlo simulations. In particular, we show that the phase boundaries between the paramagnetic state and magnetically ordered states are generically fluctuation-induced first-order phase transitions. Our results are potentially applicable to ${\mathrm{Ru}}⁴⁺$- and ${\mathrm{Ir}}⁵⁺$-based honeycomb magnets.