### Abstract

We perform an exact-diagonalization study of the spin-12 XXZ Heisenberg antiferromagnet on the kagome lattice at finite magnetization m=23 with an emphasis on the XY point (Jz=0) and in the presence of a small chiral term. Recent analytic work by Kumar et al. [K. Kumar, K. Sun, and E. Fradkin, Phys. Rev. B 90, 174409 (2014)PRBMDO1098-012110.1103/PhysRevB.90.174409] on the same model, using a newly developed flux attachment transformation, predicts a plateau at this value of the magnetization described by a chiral spin liquid (CSL) with a spin Hall conductance of σxy=12. Such a state is topological in nature, has a ground-state degeneracy, and exhibits fractional excitations. We analyze the degeneracy structure in the low-energy manifold, identify the candidate topological states, and use them to compute the modular matrices and Chern numbers, all of which strongly agree with expected theoretical behavior for the σxy=12 CSL. In the limit of zero chirality, we find on most (not all) clusters that the topological invariants are still those of a CSL.

Original language | English (US) |
---|---|

Article number | 134410 |

Journal | Physical Review B |

Volume | 94 |

Issue number | 13 |

DOIs | |

State | Published - Oct 10 2016 |

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### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

*Physical Review B*,

*94*(13), [134410]. https://doi.org/10.1103/PhysRevB.94.134410

**Numerical evidence for a chiral spin liquid in the XXZ antiferromagnetic Heisenberg model on the kagome lattice at m= 23 magnetization.** / Kumar, Krishna; Changlani, Hitesh J.; Clark, Bryan K.; Fradkin, Eduardo.

Research output: Contribution to journal › Article

*Physical Review B*, vol. 94, no. 13, 134410. https://doi.org/10.1103/PhysRevB.94.134410

}

TY - JOUR

T1 - Numerical evidence for a chiral spin liquid in the XXZ antiferromagnetic Heisenberg model on the kagome lattice at m= 23 magnetization

AU - Kumar, Krishna

AU - Changlani, Hitesh J.

AU - Clark, Bryan K.

AU - Fradkin, Eduardo

PY - 2016/10/10

Y1 - 2016/10/10

N2 - We perform an exact-diagonalization study of the spin-12 XXZ Heisenberg antiferromagnet on the kagome lattice at finite magnetization m=23 with an emphasis on the XY point (Jz=0) and in the presence of a small chiral term. Recent analytic work by Kumar et al. [K. Kumar, K. Sun, and E. Fradkin, Phys. Rev. B 90, 174409 (2014)PRBMDO1098-012110.1103/PhysRevB.90.174409] on the same model, using a newly developed flux attachment transformation, predicts a plateau at this value of the magnetization described by a chiral spin liquid (CSL) with a spin Hall conductance of σxy=12. Such a state is topological in nature, has a ground-state degeneracy, and exhibits fractional excitations. We analyze the degeneracy structure in the low-energy manifold, identify the candidate topological states, and use them to compute the modular matrices and Chern numbers, all of which strongly agree with expected theoretical behavior for the σxy=12 CSL. In the limit of zero chirality, we find on most (not all) clusters that the topological invariants are still those of a CSL.

AB - We perform an exact-diagonalization study of the spin-12 XXZ Heisenberg antiferromagnet on the kagome lattice at finite magnetization m=23 with an emphasis on the XY point (Jz=0) and in the presence of a small chiral term. Recent analytic work by Kumar et al. [K. Kumar, K. Sun, and E. Fradkin, Phys. Rev. B 90, 174409 (2014)PRBMDO1098-012110.1103/PhysRevB.90.174409] on the same model, using a newly developed flux attachment transformation, predicts a plateau at this value of the magnetization described by a chiral spin liquid (CSL) with a spin Hall conductance of σxy=12. Such a state is topological in nature, has a ground-state degeneracy, and exhibits fractional excitations. We analyze the degeneracy structure in the low-energy manifold, identify the candidate topological states, and use them to compute the modular matrices and Chern numbers, all of which strongly agree with expected theoretical behavior for the σxy=12 CSL. In the limit of zero chirality, we find on most (not all) clusters that the topological invariants are still those of a CSL.

UR - http://www.scopus.com/inward/record.url?scp=84992088964&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84992088964&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.94.134410

DO - 10.1103/PhysRevB.94.134410

M3 - Article

AN - SCOPUS:84992088964

VL - 94

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 13

M1 - 134410

ER -