Non-Abelian chiral spin liquid in a spin-$1$ antiferromagnet on the square lattice
Abstract
Non-Abelian chiral spin liquids (CSLs) host non-Abelian anyon excitations and are promising platforms for topological quantum computation. However, realizing non-Abelian CSLs in short-range interacting spin systems remains elusive. Here, we study a spin-$1$ square-lattice model with the first- and second-neighbor bilinear (J1,J2) and biquadratic interactions (K1,K2), as well as the three-spin scalar chiral coupling Jχ. Inspired by the evidence of the Moore-Read state in exact diagonalization and infinite Projected Entangled Pair States calculations, we fix J1=1.0, J2/J1=0.623, K1/J1=−0.176, and obtain a quantum phase diagram for 0 ≤ K2/J1 ≤ 0.4 and 0.3 ≤ Jχ/J1 ≤ 0.6 by using the density matrix renormalization group (DMRG) calculations. We identify a stripe antiferromagnetic phase, a Néel antiferromagnetic phase, a magnetically ordered chiral spin state phase, and a non-Abelian CSL phase emerging near the boundaries of the ordered phases. The unbiased DMRG results provide strong evidence for the Moore-Read state, including the three topological sectors, the quantized spin Chern number C=1, and the level counting of low-lying entanglement spectra which is consistent with the chiral SU(2)2 conformal field theory. Our results may shed new light on searching for non-Abelian CSLs in other higher-spin (S > 1/2) systems with short-range couplings.
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BibTeX
@misc{zhang2026nonabelian,
title = {{Non-Abelian chiral spin liquid in a spin-$1$ antiferromagnet on the square lattice}},
author = {Xiao-Tian Zhang and Yuan Yang and D. N. Sheng and Shou-Shu Gong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15061},
eprint = {2609.15061},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15061},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-Abelian chiral spin liquid in a spin-$1$ antiferromagnet on the square lattice
AU - Xiao-Tian Zhang
AU - Yuan Yang
AU - D. N. Sheng
AU - Shou-Shu Gong
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15061
UR - https://arxiv.org/abs/2609.15061
AB - Non-Abelian chiral spin liquids (CSLs) host non-Abelian anyon excitations and are promising platforms for topological quantum computation. However, realizing non-Abelian CSLs in short-range interacting spin systems remains elusive. Here, we study a spin-$1$ square-lattice model with the first- and second-neighbor bilinear (J_1,J_2) and biquadratic interactions (K_1,K_2), as well as the three-spin scalar chiral coupling J_χ. Inspired by the evidence of the Moore-Read state in exact diagonalization and infinite Projected Entangled Pair States calculations, we fix J_1=1.0, J_2/J_1=0.623, K_1/J_1=−0.176, and obtain a quantum phase diagram for 0 ≤ K_2/J_1 ≤ 0.4 and 0.3 ≤ J_χ/J_1 ≤ 0.6 by using the density matrix renormalization group (DMRG) calculations. We identify a stripe antiferromagnetic phase, a Néel antiferromagnetic phase, a magnetically ordered chiral spin state phase, and a non-Abelian CSL phase emerging near the boundaries of the ordered phases. The unbiased DMRG results provide strong evidence for the Moore-Read state, including the three topological sectors, the quantized spin Chern number C=1, and the level counting of low-lying entanglement spectra which is consistent with the chiral SU(2)_2 conformal field theory. Our results may shed new light on searching for non-Abelian CSLs in other higher-spin (S > 1/2) systems with short-range couplings.
ER -