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arXiv:2108.06676 · Physical review. B./Physical review. B

Coexistence of non-Abelian chiral spin liquid and magnetic order in a spin-1 antiferromagnet

Yixuan Huang, Wei Kang Zhu, Shou-Shu Gong, Hong‐Chen Jiang, D. N. Sheng

Published Apr 4, 2022• 15 citations
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Abstract

We study the ground-state properties of a spin-1 Heisenberg model on a square lattice with the first- and second-nearest-neighbor antiferromagnetic couplings ${J}_{1}$ and ${J}_{2}$ and a three-spin scalar chirality term ${J}_{\ensuremath{\chi}}$. Using the density matrix renormalization group calculation, we map out a global phase diagram including various magnetic order phases and an emergent quantum spin liquid phase. The nature of the spin liquid is identified as a bosonic non-Abelian Moore-Read state from the fingerprint of the entanglement spectra and identification of a full set of topological sectors. We further unveil a stripe magnetic order coexisting with this spin liquid. Our results not only establish a rare example of non-Abelian spin liquids in simple spin systems but also demonstrate the coexistence of fractionalized excitations and magnetic order beyond mean-field descriptions.

DOI
10.1103/physrevb.105.155104

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We study the ground-state properties of a spin-1 Heisenberg model on a square lattice with the first- and second-nearest-neighbor antiferromagnetic couplings J1{J}_{1}J1​ and J2{J}_{2}J2​ and a three-spin scalar chirality term J\ensuremathχ{J}_{\ensuremath{\chi}}J\ensuremathχ​. Using the density matrix renormalization group calculation, we map out a global phase diagram including various magnetic order phases and an emergent quantum spin liquid phase. The nature of the spin liquid is identified as a bosonic non-Abelian Moore-Read state from the fingerprint of the entanglement spectra and identification of a full set of topological sectors. We further unveil a stripe magnetic order coexisting with this spin liquid. Our results not only establish a rare example of non-Abelian spin liquids in simple spin systems but also demonstrate the coexistence of fractionalized excitations and magnetic order beyond mean-field descriptions.
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Since strong quantum fluctuations are essential for the emergence of quantum spin liquids, there have been extensive exploration and identification of spin liquid candidates in spin-12\frac{1}{2}21​ systems, while such activities are rare in higher spin systems. Here we report an example of non-Abelian chiral spin liquid emerging in a spin-32\frac{3}{2}23​ Heisenberg model on a square lattice. By tuning Heisenberg exchange interaction and scalar chirality interaction, we map out a quantum phase diagram enclosing three conventional magnetic orders and a chiral spin liquid based on density-matrix renormalization group studies. The nature of the spin liquid is identified as a long-sought bosonic version of the Read-Rezayi state that supports non-Abelian Fibonacci anyonic statistics, identified by the ground state entanglement spectrum. Significantly, we establish that the non-Abelian chiral spin liquid emerges through the enlarged local degrees of freedom and enhanced quantum fluctuations near the classical phase boundaries of competing magnetic orders. Our numerical discovery of an exotic quantum spin liquid in a spin-32\frac{3}{2}23​ system suggests a route for discovering fractionalized quantum phases in frustrated higher spin magnetic compounds.
A chiral spin liquid (CSL) is an analog of the fractional quantum Hall state in spin systems. Recently, an interesting topic has been the coexistence of CSL and magnetic order, which is beyond the conventional understanding of the spin liquid. Here, the authors examine possible phase coexistence in the spin-\textonehalf{} square-lattice J1{J}_{1}J1​-J2{J}_{2}J2​-${J}_{\ensuremath{\chi}}$ model, by using unbiased density matrix renormalization group calculations. The numerical data identify the CSL but find no evidence for the phase coexistence that was conjectured by mean-field calculations.
Topological Spin Liquid Phase in the Spin-1/21/21/2 Triangular Heisenberg Model
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