Stability of the 1/3 magnetization plateau of the $J_1-J_2$ kagome Heisenberg model

In this study, we investigate the finite-temperature properties of the spin-1/2 $J_1-J_2$ Heisenberg model on the kagome lattice using the orthogonalized finite-temperature Lanczos method. Under a zero magnetic field, the specific heat exhibits a double-peak structure, as $\mathrm{\mid }{J}_2\mathrm{\mid }$ increases. Additionally, at approximately $J_2=0$, the magnetic entropy remains finite, even at low temperatures. The finite-temperature magnetization curve reveals the asymmetric melting behavior of the 1/3 plateau around $J_2=0$. As $\mathrm{\mid }{J}_2\mathrm{\mid }$ increases, the 1/3 plateau becomes more stable, exhibiting symmetric melting behavior. Specifically, for $J_2>0$, the $\mathbf{Q}=\mathbf{0}$ up-up-down structure is stabilized, whereas for $J_2<0$, the $\sqrt{3}\times \sqrt{3}$ up-up-down structure is stabilized.