Chiral and Critical Spin Liquids in Spin-$1/2$ Kagome Antiferromagnet

TL;DR

This paper investigates the quantum phase transitions between different spin liquid states in a spin-1/2 kagome antiferromagnet, revealing a transition from a chiral topological state to a critical gapless state driven by specific couplings.

Contribution

It identifies and characterizes a chiral spin liquid with fractional quantum Hall features and elucidates the nature of the transition to a critical spin liquid in the kagome antiferromagnet.

Findings

Chiral spin liquid characterized by fractional Chern number and edge spectrum.

Critical spin liquid with gapless excitations adjacent to the chiral phase.

Quantum phase transition driven by neutral excitation gap collapse.

Abstract

The topological quantum spin liquids (SL) and the nature of quantum phase transitions between them have attracted intensive attentions for the past twenty years. The extended kagome spin-1/2 antiferromagnet emerges as the primary candidate for hosting both time reversal symmetry (TRS) preserving and TRS breaking SLs based on density matrix renormalization group simulations. To uncover the nature of the novel quantum phase transition between the SL states, we study a minimum XY model with the nearest neighbor (NN) ($J_{xy}$), the second and third NN couplings ($J_{2xy}=J_{3xy}=J'_{xy}$). We identify the TRS broken chiral SL (CSL) with the turn on of a small perturbation $J'_{xy}\sim 0.06 J_{xy}$, which is fully characterized by the fractionally quantized topological Chern number and the conformal edge spectrum as the $\nu=1/2$ fractional quantum Hall state. On the other hand, the NN XY model ($J'_{xy}=0$) is shown to be a critical SL state adjacent to the CSL, characterized by the gapless spin singlet excitations and also vanishing small spin triplet excitations. The quantum phase transition from the CSL to the gapless critical SL is driven by the collapsing of the neutral (spin singlet) excitation gap. By following the evolution of entanglement spectrum, we find that the transition takes place through the coupling of the edge states with opposite chiralities, which merge into the bulk and become gapless neutral excitations. The effect of the NN spin-$z$ coupling $J_z$ is also studied, which leads to a quantum phase diagram with an extended regime for the gapless SL.