Possible chiral spin liquid state in the $S=1/2$ kagome Heisenberg model

TL;DR

This study provides numerical evidence suggesting that the ground state of the $S=1/2$ kagome Heisenberg antiferromagnet may be a stable chiral spin liquid, characterized by spontaneous time-reversal symmetry breaking and complex phase behavior.

Contribution

The paper demonstrates the stability of a chiral spin liquid phase in the kagome Heisenberg model using advanced numerical and analytical methods, expanding understanding of its ground state.

Findings

Evidence of a stable chiral spin liquid phase.

Identification of ground-state degeneracy from symmetry breaking.

Phase diagram includes magnetically ordered and valence-bond crystal phases.

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 might be a chiral spin liquid. Combining the density matrix renormalization group method and 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. We characterize the nature of the ground state by computing energy derivatives, revealing ground-state degeneracy arising from spontaneous breaking of 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.