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

doi:10.1103/physrevb.94.134410

Title: Numerical evidence for a chiral spin liquid in the XXZ antiferromagnetic Heisenberg model on the kagome lattice at $m = \frac{2}{3}$ magnetization

Journal Article · Mon Oct 10 00:00:00 EDT 2016 · Physical Review B

DOI:https://doi.org/10.1103/physrevb.94.134410· OSTI ID:1535771

Kumar, Krishna ^[1]; Changlani, Hitesh J. ^[1]; Clark, Bryan K. ^[1]; Fradkin, Eduardo ^[1]

Univ. of Illinois at Urbana-Champaign, IL (United States). Inst. for Condensed Matter Theory

In this work, 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 $X Y$ 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 $σ_{x y} = \frac{1}{2}$ . 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 $σ_{x y} = \frac{1}{2}$ CSL. In the limit of zero chirality, we find on most (not all) clusters that the topological invariants are still those of a CSL.

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Research Organization:: Univ. of Illinois at Urbana-Champaign, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC); National Science Foundation (NSF)

Grant/Contract Number:: SC0008692; FG02-12ER46875; DMR 1408713; OCI-0725070; ACI-1238993

OSTI ID:: 1535771

Alternate ID(s):: OSTI ID: 1328589

Journal Information:: Physical Review B, Vol. 94, Issue 13; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 9 works

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Title: Numerical evidence for a chiral spin liquid in the XXZ antiferromagnetic Heisenberg model on the kagome lattice at m = 2 3 magnetization

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Title: Numerical evidence for a chiral spin liquid in the XXZ antiferromagnetic Heisenberg model on the kagome lattice at $m = \frac{2}{3}$ magnetization