Possible chiral spin liquid state in the S = 1/2 kagome Heisenberg model
Rong-Yang Sun, Hui-Ke Jin, Hong-Hao Tu, Yi Zhou
Abstract
Abstract 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 $$\sqrt{3}\times \sqrt{3}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msqrt> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msqrt> <mml:mo>×</mml:mo> <mml:msqrt> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msqrt> </mml:mrow> </mml:math> magnetically ordered phase and two valence-bond crystal phases.