Exploring the J₁-J₂Heisenberg magnetization curve with Gutzwiller-projected Abrikosov fermions

We investigate the magnetization curves of the Heisenberg model on the triangular lattice, incorporating both nearest-neighbor (J₁) and next-nearest-neighbor (J₂) superexchange couplings. Our results are obtained using variational wave functions constructed via Abrikosov fermions. We consider several Ansatze to describe different spin arrangements. In the weakly-frustrated regime (e.g., J₂=0), our findings confirm previous calculations: a finite magnetic field induces a Y state, which persists up to the 1/3 magnetization plateau. Most interestingly, in the highly-frustrated regime (e.g., J₂/J₁=1/8), the Dirac spin liquid stabilized at zero field leads to an extended region where the gauge flux is self-adjusted. This mechanism results in a zero-energy Landau level that is fully occupied by one spin species (e.g., spin-up) and entirely empty for the other (spin-down).The relevance of these results is briefly discussed in connection with recent experiments.