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. ^[2]; Clark, Bryan K. ^[2]; Fradkin, Eduardo ^[2]

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1. Univ. of Illinois at Urbana-Champaign, IL (United States). Inst. for Condensed Matter Theory; DOE/OSTI
2. 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 $XY$ point $\left(J_z=0\right)$ 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 ${\sigma }_{xy}=\frac{1}{2}$ . 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 ${\sigma }_{xy}=\frac{1}{2}$ CSL. In the limit of zero chirality, we find on most (not all) clusters that the topological invariants are still those of a CSL.

• Research Organization: Univ. of Illinois at Urbana-Champaign, IL (United States)
• Sponsoring Organization: National Science Foundation (NSF); USDOE; USDOE Office of Science (SC)
• Grant/Contract Number: SC0008692
• OSTI ID: 1535771
• Alternate ID(s): OSTI ID: 1328589
• Journal Information: Physical Review B, Journal Name: Physical Review B Journal Issue: 13 Vol. 94; ISSN 2469-9950; ISSN PRBMDO
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Heisenberg model
Kagome lattice
XY model
exact diagonalization
quantum spin liquid
topological phases of matter