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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

Abstract

In this work, we perform an exact-diagonalization study of the spin- 1 2 XXZ Heisenberg antiferromagnet on the kagome lattice at finite magnetization m = 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 = 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 = 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.

Authors:
 [1];  [1];  [1];  [1]
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  1. Univ. of Illinois at Urbana-Champaign, IL (United States). Inst. for Condensed Matter Theory
Publication Date:
Research Org.:
Univ. of Illinois at Urbana-Champaign, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC); National Science Foundation (NSF)
OSTI Identifier:
1535771
Alternate Identifier(s):
OSTI ID: 1328589
Grant/Contract Number:  
SC0008692; FG02-12ER46875; DMR 1408713; OCI-0725070; ACI-1238993
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 94; Journal Issue: 13; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; quantum spin liquid; topological phases of matter; Kagome lattice; exact diagonalization; Heisenberg model; XY model

Citation Formats

Kumar, Krishna, Changlani, Hitesh J., Clark, Bryan K., and Fradkin, Eduardo. Numerical evidence for a chiral spin liquid in the XXZ antiferromagnetic Heisenberg model on the kagome lattice at m=23 magnetization. United States: N. p., 2016. Web. doi:10.1103/physrevb.94.134410.
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Kumar, Krishna, Changlani, Hitesh J., Clark, Bryan K., & Fradkin, Eduardo. Numerical evidence for a chiral spin liquid in the XXZ antiferromagnetic Heisenberg model on the kagome lattice at m=23 magnetization. United States. https://doi.org/10.1103/physrevb.94.134410
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Kumar, Krishna, Changlani, Hitesh J., Clark, Bryan K., and Fradkin, Eduardo. Mon . "Numerical evidence for a chiral spin liquid in the XXZ antiferromagnetic Heisenberg model on the kagome lattice at m=23 magnetization". United States. https://doi.org/10.1103/physrevb.94.134410. https://www.osti.gov/servlets/purl/1535771.
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@article{osti_1535771,
title = {Numerical evidence for a chiral spin liquid in the XXZ antiferromagnetic Heisenberg model on the kagome lattice at m=23 magnetization},
author = {Kumar, Krishna and Changlani, Hitesh J. and Clark, Bryan K. and Fradkin, Eduardo},
abstractNote = {In this work, 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)] 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.},
doi = {10.1103/physrevb.94.134410},
journal = {Physical Review B},
number = 13,
volume = 94,
place = {United States},
year = {Mon Oct 10 00:00:00 EDT 2016},
month = {Mon Oct 10 00:00:00 EDT 2016}
}
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https://doi.org/10.1103/physrevb.94.134410
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    Works referencing / citing this record:

    Topological approach to quantum liquid ground states on geometrically frustrated Heisenberg antiferromagnets
    journal, January 2020

    • Pal, Santanu; Mukherjee, Anirban; Lal, Siddhartha
    • Journal of Physics: Condensed Matter, Vol. 32, Issue 16
    • DOI: 10.1088/1361-648x/ab670f

    Correlated spin liquids in the quantum kagome antiferromagnet at finite field: a renormalization group analysis
    journal, February 2019

    • Pal, Santanu; Mukherjee, Anirban; Lal, Siddhartha
    • New Journal of Physics, Vol. 21, Issue 2
    • DOI: 10.1088/1367-2630/ab05ff

    Quantum spin circulator in Y junctions of Heisenberg chains
    journal, June 2018

    Resonating quantum three-coloring wave functions for the kagome quantum antiferromagnet
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    Emergent Chiral Spin State in the Mott Phase of a Bosonic Kane-Mele-Hubbard Model
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