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arXiv:1410.4883 · Physical Review B

Chiral and critical spin liquids in a spin- 12 kagome antiferromagnet

Wei Kang Zhu, Shou-Shu Gong, D. N. Sheng

Published Jul 28, 2015• 38 citations
arXivHTMLPDF

Abstract

The kagome spin-$\frac{1}{2}$ systems have attracted intensive attention in recent years as the primary candidate for hosting different gapped spin liquids (SLs). 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-NN, and the third-NN couplings (${J}_{2xy}={J}_{3xy}={J}_{xy}^{\ensuremath{'}}$). We identify the time-reversal-symmetry-broken chiral SL (CSL) with the turn on of a small perturbation ${J}_{xy}^{\ensuremath{'}}\ensuremath{\sim}0.06{J}_{xy}$, which is fully characterized by the fractionally quantized topological Chern number and the conformal edge spectrum as the $\ensuremath{\nu}=1/2$ fractional quantum Hall state. Interestingly, the NN $XY$ model (${J}_{xy}^{\ensuremath{'}}=0$) is shown to be a critical SL state adjacent to the CSL, characterized by the gapless spin singlet and 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. 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.

DOI
10.1103/physrevb.92.014424

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The fractional quantum Hall effect (FQHE) realized in two-dimensional electron systems under a magnetic field is one of the most remarkable discoveries in condensed matter physics. Interestingly, it has been proposed that FQHE can also emerge in time-reversal invariant spin systems, known as the chiral spin liquid (CSL) characterized by the topological order and the emerging of the fractionalized quasiparticles. A CSL can naturally lead to the exotic superconductivity originating from the condense of anyonic quasiparticles. Although CSL was highly sought after for more than twenty years, it had never been found in a spin isotropic Heisenberg model or related materials. By developing a density-matrix renormalization group based method for adiabatically inserting flux, we discover a FQHE in a spin-½ isotropic kagome Heisenberg model. We identify this FQHE state as the long-sought CSL with a uniform chiral order spontaneously breaking time reversal symmetry, which is uniquely characterized by the half-integer quantized topological Chern number protected by a robust excitation gap. The CSL is found to be at the neighbor of the previously identified Z2 spin liquid, which may lead to an exotic quantum phase transition between two gapped topological spin liquids.
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