Variational Monte Carlo Study of the 1/9 Magnetization Plateau in Kagome Antiferromagnets

Abstract: Motivated by very recent experimental observations of the 1/9 magnetization plateaus in YCu$3$(OH)${6+x}$Br${3-x}$ and YCu$_3$(OD)${6+x}$Br$_{3-x}$, our study delves into the magnetic field-induced phase transitions in the nearest-neighbor antiferromagnetic Heisenberg model on the kagome lattice using the variational Monte Carlo technique. We uncover a phase transition from a zero-field Dirac spin liquid to a field-induced magnetically disordered phase that exhibits the 1/9 magnetization plateau. Through a comprehensive analysis encompassing the magnetization distribution, spin correlations, chiral order parameter, topological entanglement entropy, ground-state degeneracy, Chern number and excitation spectrum, we pinpoint the phase associated with this magnetization plateau as a chiral $\mathbb{Z}_3$ topological quantum spin liquid and elucidate its diverse physical properties.