arXiv:cond-mat/0412608 · Physica B Condensed Matter

Ground state and low-lying excitations of the spin- XXZ model on the kagomé lattice at magnetization

A. Honecker, D. C. Cabra, Marcelo D. Grynberg, P. C. W. Holdsworth, Pierre Pujol, Johannes Richter, D. Schmalfuß, J. Schulenburg

Published Mar 3, 2005• 7 citations

arXiv HTML PDF

DOI: 10.1016/j.physb.2005.01.430

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arXiv:cond-mat/0412608 · Physica B Condensed Matter

Ground state and low-lying excitations of the spin- XXZ model on the kagomé lattice at magnetization

A. Honecker, D. C. Cabra, Marcelo D. Grynberg, P. C. W. Holdsworth, Pierre Pujol, Johannes Richter, D. Schmalfuß, J. Schulenburg

Published Mar 3, 2005• 7 citations

arXiv HTML PDF

DOI: 10.1016/j.physb.2005.01.430

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We perform an exact-diagonalization study of the spin- $\frac{1}{2}$ XXZ Heisenberg antiferromagnet on the kagome lattice at finite magnetization $m=\frac{2}{3}$ with an emphasis on the $XY$ point $({J}_{z}=0)$ 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)] 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 ${\ensuremath{\sigma}}_{xy}=\frac{1}{2}$. 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 ${\ensuremath{\sigma}}_{xy}=\frac{1}{2}$ CSL. In the limit of zero chirality, we find on most (not all) clusters that the topological invariants are still those of a CSL.We perform an exact-diagonalization study of the spin-$\frac{1}{2}$ XXZ Heisenberg antiferromagnet on the kagome lattice at finite magnetization $m=\frac{2}{3}$ with an emphasis on the $XY$ point $({J}_{z}=0)$ 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)] 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 ${\ensuremath{\sigma}}_{xy}=\frac{1}{2}$. 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 ${\ensuremath{\sigma}}_{xy}=\frac{1}{2}$ CSL. In the limit of zero chirality, we find on most (not all) clusters that the topological invariants are still those of a CSL.

arXiv:1606.04103Physical review. B./Physical review. BOct 10, 201616 citations

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Ch. Waldtmann, H. U. Everts, B. Bernu +4 more

arXiv:cond-mat/9802168The European Physical Journal BMay 1, 1998375 citations

We perform an exact-diagonalization study of the spin-

\frac{1}{2}

XXZ Heisenberg antiferromagnet on the kagome lattice at finite magnetization

m=\frac{2}{3}

with an emphasis on the

XY

point

({J}_{z}=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)] 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 ${\ensuremath{\sigma}}_{xy}=\frac{1}{2}$. 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 ${\ensuremath{\sigma}}_{xy}=\frac{1}{2}$ CSL. In the limit of zero chirality, we find on most (not all) clusters that the topological invariants are still those of a CSL.