The nature of the ground state for the S = 1/2 Kagome Heisenberg antiferromagnet (KHAF) has been elusive. We revisit this challenging problem and provide numerical evidence that its ground state is a chiral spin liquid. Combining the density matrix renormalization group method with analytical analyses, we demonstrate that the previously observed chiral spin liquid phase in the KHAF with longer-range couplings is stable in a broader region of the phase diagram. We characterize the nature of the ground state by computing energy derivatives, revealing the ground-state degeneracy arising from the spontaneous breaking of the time-reversal symmetry, and targeting the semion sector. We further investigate the phase diagram in the vicinity of the KHAF and observe a \(\sqrt{3}\times \sqrt{3}\) magnetically ordered phase and two valence-bond crystal phases.

S = 1/2 Kagome 海森堡反铁磁体 (KHAF)的基态性质 一直难以捉摸。我们重新审视这个具有挑战性的问题，并提供数值证据证明其基态是手性自旋液体。将密度矩阵重正化群方法与分析分析相结合，我们证明了先前观察到的具有长程耦合的 KHAF 中的手性自旋液相在相图的更广泛区域中是稳定的。我们通过计算能量导数来表征基态的性质，揭示时间反转对称性自发破缺引起的基态简并性，并针对半子扇区。我们进一步研究了 KHAF 附近的相图，并观察到​​\(\sqrt{3}\times \sqrt{3}\)磁有序相和两个价键晶相。